In existing studies on neural networks (NNs) stabilization, stochastic disturbances are typically regarded as negative factors. In contrast, this paper systematically explores the positive role of stochastic disturbances in the stabilization of NNs and proposes a novel finite-time noise feedback control method. By rationally utilizing stochastic disturbances, the originally unstable fuzzy memristive NNs with reaction-diffusion components achieve finite-time stochastic stabilization. Meanwhile, some less conservative finite-time stabilization criteria are proposed, eliminating the requirement in classical criteria that Lyapunov function’s differential operator must be strictly negative. The novel criteria not only extend the application scope of existing stochastic stabilization from exponential stabilization to finite-time case, but also elaborately explore the relationship between noise intensity and the convergence speed of the system. Finally, the effectiveness of derived results is verified through simulation.

This article focuses on the low-conservative stability criteria of delayed neural networks (DNNs). To achieve this goal, new techniques are developed to effectively utilize more system-related information. To use the time-varying delay information, some delay-product terms are introduced into the Lyapunov-Krasovskii functional (LKF), and an extended matrix-injection-based transformation method, which introduces delay-derivative-dependent slack matrices while obtaining the negative definite condition, is proposed. With respect to the use of activation function information, the terms related to the activation function are fully augmented in the LKF. In particular, by considering the sector-constraint information of the activation function, a new nonlinear-function-dependent functional term is established, and a sector-constraint-dependent matrix-separation-based inequality is developed. By applying the above techniques, several improved stability criteria are derived, and two typical examples are provided to illustrate the advantages of the proposed methods.

This article investigates the practically predefined-time stabilization issue of fuzzy memristive neural networks (FMNNs) in the presence of stochastic disturbances and random deception attacks (RDAs). First, in this article, the concept of practically predefined-time stabilization in probability (PPDTSP) of FMNNs is introduced, and a novel Lyapunov-type criterion for PPDTSP is proposed. The novel criterion eases the restrictions on the differential operator of the Lyapunov function and can be reduced to the existing criterion of predefined-time stabilization in probability (PDTSP). Then, a simplified, practically predefined-time control scheme is constructed to ensure PPDTSP of FMNNs under the interference of stochastic disturbances and RDAs. Furthermore, by employing the simplified control scheme and in the absence of RDAs, some PDTSP results are presented as special instances of the PPDTSP conclusions given in this article. Finally, numerical simulations are conducted to validate the accuracy of the theoretical results.

This article focuses on the problem of $N$ -step model predictive control (MPC) under a mixed time/event-triggered encoding-decoding strategy for polytopic uncertain systems with hard constraints. A staged requirements-dependent mixed time/event-triggered mechanism (MTEM) is proposed. When the system state is outside the terminal constraint set (TCS), the time-triggered pattern is implemented to meet the staged requirement of improving control performance. When the system state is in the TCS, an event-triggered pattern is used to fulfill the staged requirement of conserving resources. The event-triggered pattern contains an adaptively adjusting variable related to the "distance" of the system state from the TCS core, which helps meet the relative staged requirements in the TCS. The staged requirements-dependent MTEM-based encoding-decoding strategy improves the communication security while saving computational resources for encoding and decoding, as well as network resources. Based on two offline optimization problems (OPs), the TCS and the approximate robust one-step sets are designed, respectively. The control laws outside the TCS are obtained by an online OP. A mixed time/event-triggered encoding-decoding-based $N$ -step MPC algorithm is proposed based on three OPs. The algorithm's feasibility and the input-to-state stability of the closed-loop system are analyzed. Two examples are presented to illustrate the effectiveness and superiority of the proposed MTEM and MPC algorithm in saving resources while ensuring control performance.

This paper investigates the fixed/prescribed-time synchronization problem for fuzzy inertial memristive neural networks (FIMNNs) with hybrid delays. Within a unified framework, a comparative study was conducted on the interval matrix method and the maximum absolute value method with respect to the state-dependent switching parameters induced by memristive characteristics. Correspondingly, two different controllers are designed, with theorem constraints expressed algebraically and as LMIs. Numerical experiments demonstrate that, under identical initial system parameters, the interval matrix method constructs a Lyapunov–Krasovskii functional (LKF) incorporating an integral term, enabling finer handling of time-delay effects. As a result, it provides a more accurate estimate of the upper bound of the settling time (ST) compared to the maximum absolute value method, thereby achieving faster and more efficient synchronization control. Ultimately, the proposed results are applied to image encryption, thereby demonstrating its theoretical significance and practical utility.

This article develops a robust economic model predictive control (EMPC) scheme for load frequency control (LFC) in multiarea smart grids with load disturbances. The proposed approach integrates the optimization of the cost and the utilization efficiency of network resources within a single EMPC framework. An economic cost function, including the generation cost and the LFC cost, is designed to minimize the involved costs. To optimize the utilization efficiency of network resources while maintaining satisfactory control performance, a new dynamic memory event-triggered mechanism (DMETM) is designed. By introducing a dynamic variable and an adaptively adjusting variable, the proposed DMETM adaptively adjusts triggering conditions using historical triggering information, thereby conserving network resources and reducing communication burden. A “min–max” EMPC optimization problem (OP) is developed, and it is transformed into an auxiliary OP based on linear matrix inequalities. The recursive feasibility of the auxiliary OP is proved, and the closed-loop system is also proven to satisfy input-to-state practical stability, guaranteeing robustness against the load disturbances. At last, a case study on a three-area smart grids verifies the effectiveness and the advantages of the proposed DMETM-based EMPC scheme and demonstrates its potential in enhancing the optimization of the economic cost and the utilization efficiency of network resources.

This article investigates the practical fixed-time synchronization (FxTS) for complex dynamical networks (CDNs). Given the notable benefits associated with intermittent control, wherein control inputs are activated solely during the working phase of each control cycle, and event-triggered control, which significantly curtails the frequency of control input updates, this article proposes an intermittent event-triggered control scheme aimed at achieving practical FxTS in CDNs. The proposed scheme substantially mitigates the volume of information transmitted across the network while concurrently reducing control-related expenditures. To mitigate the issue of high-frequency buffeting, the newly devised control scheme employs a saturation function as a substitute for the conventional signum function. Subsequently, this article presents a more precise estimation approach for reasonably approximating the synchronization time (ST) of CDNs and the synchronization error (SE) induced by the integration of the saturation function. Moreover, this article imposes constraints on the frequency and total duration of communication pauses in an average-sense manner and constructs a piecewise Lyapunov function to further deduce several less conservative criteria for practical FxTS. Finally, two illustrative examples are provided to demonstrate the viability of the intermittent event-triggered control scheme and the accuracy of the ST and SE estimations.

This article addresses the problem of fixed-time bipartite synchronization (FxTBS) of signed networks (SNs) affected by impulses. First, this article constructs a model of SNs that captures the multilayer properties of the network and takes into account the influence of nonlinear coupling strengths between nodes. To overcome the challenges brought by the introduction of nonlinear coupling strengths, this article adopts a Takagi–Sugeno fuzzy model to characterize the nonlinear variation of coupling strengths reasonably. Then, in the framework of average impulsive interval applicable to a wider range of impulsive signals, this article proposes a novel method for analyzing the fixed-time stability of impulsive systems, which not only loosens the restriction of the derivative of the Lyapunov function in the existing studies, but also gives a more accurate estimation of the settling time, and more importantly, provides a theoretical basis for designing appropriate impulsive signals to modulate the dynamic behavior of SNs toward achieving the desired goal. Based on the newly suggested method, this article derives a unified synchronization criterion suitable for evaluating the implementation of FxTBS of SNs under both desynchronizing and synchronizing impulses. Finally, this article visualizes the correctness of the aforementioned theoretical results utilizing a widely used numerical example.

In this article, the problem of multistep model predictive control (MPC) under a mixed time/event-triggered mechanism (MTEM) is investigated for fuzzy systems with hard constraints. To improve its flexibility in adjusting releases, this MTEM incorporates the information from the fuzzy membership functions and the terminal constraint set (TCS). In the online control unit, the time-triggered way is first implemented to steer the system state into the TCS quickly, and then in the offline control unit, the involved event-triggered pattern plays its role in conserving resources while ensuring the control performance. Two offline optimization problems (OPs) are presented to design the TCS and the approximate robust one step sets, respectively, and an online OP is given to design the control laws to steer the system state into TCS. Based on these three OPs, we propose an MTEM-based multistep fuzzy MPC algorithm and demonstrate the feasibility of the algorithm together with the input-to-state stability of the closed-loop system. Three examples are given to verify the effectiveness of the proposed method and its superiority in saving communication and computing resources while ensuring control performance.

This article investigates the multistep model predictive load frequency control problem for multiarea smart grids (MASGs) with wind power and air conditioning loads under false data injection attack, where a control performance standards (CPSs)-dependent dynamic event-triggered mechanism (DETM) is considered to manage the data transmission. The CPSs-dependent DETM contains an adaptive adjustment variable related to two CPSs on the frequency deviation and area control error, which helps it to effectively reduce unnecessary transmission of data packets while promising the required frequency and tie-lie power of the MASGs. Two off-line optimization problems (OPs) are applied to design the terminal constraint set (TCS) and the approximate one step sets, respectively. The control laws designed by an online OP are utilized outside of the TCS. A CPSs-dependent DETM-based multistep MPC algorithm is proposed on the basis of the three OPs. The analyses of the feasibility of the algorithm and the stability of the closed-loop system are given. The effectiveness and superiority of the designed CPSs-dependent DETM and dynamic event-based multistep MPC algorithm are verified in two case studies of two-area and three-area smart grids.

The stability and${\mathcal {H}}_\infty$filtering for delayed discrete-time T-S fuzzy systems are studied in this article. The primary objective is to obtain less conservative and more effective analysis and design methods by exploring a combination of the characteristics of T-S fuzzy systems and the delay-dependent methods. First, as the first step of the Lyapunov–Krasovskii functional (LKF) method, a membership-dependent (MD) LKF with delay-product-type term is established to contain more delay and membership function information. Then, to obtain the negative definite condition of the forward difference of the constructed functional, an MD-matrix-separation-based inequality is developed to obtain tighter estimations for the augmented summation terms and an MD-variable-augmented-based free-weighting matrix method is proposed to avoid the generation of delay-dependent nonlinear terms. Based on the abovementioned methods, a less conservative stability criterion and an${\mathcal {H}}_\infty$fuzzy filter design method are proposed. Finally, the merits of the proposed methods are verified via two examples.

This article concentrates on the fixed-time synchronization (FxTS) problem for fuzzy complex dynamical networks (CDNs) with reaction-diffusion terms and multiple weights. First, a novel fixed-time convergence method is proposed, which relaxes the constraint on the derivative of the constructed Lyapunov functional and incorporates some of the existing results as special cases. Then, an intermittent pinning control scheme is designed to make the state trajectories of all nodes of fuzzy CDNs converge to the equilibrium point within a fixed time, which greatly reduces the control cost. On the basis of the newly presented convergence method and control scheme, several easy-to-verify criteria in the form of linear matrix inequalities are provided to guarantee the FxTS for fuzzy CDNs, and a more accurate estimation of the settling time is obtained. Finally, two examples are given to clarify the correctness of the established theoretical results.

Taking into account the infinite distributed delays and reaction-diffusions, this article investigates the global exponential synchronization problem of a class of memristor-based competitive neural networks (MCNNs) with different time scales. Based on the Lyapunov-Krasovskii functional and inequality approach, an adaptive control approach is proposed to ensure the exponential synchronization of the addressed drive-response networks. The closed-loop system is a discontinuous and delayed partial differential system in a cascade form, involving the spatial diffusion, the infinite distributed delays, the parametric adaptive law, the state-dependent switching parameters, and the variable structure controllers. By combining the theories of nonsmooth analysis, partial differential equation (PDE) and adaptive control, we present a new analytical method for rigorously deriving the synchronization of the states of the complex system. The derived m-norm (m ≥ 2)-based synchronization criteria are easily verified and the theoretical results are easily extended to memristor-based neural networks (NNs) without different time scales and reaction-diffusions. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results.

The classical results of fixed-time stabilization (FxTS) are generally achieved via nonintermittent control, as well as cannot be employed to deal with discontinuous systems and strictly intermittent control. In this article, we establish a novel FxTS method for analyzing fixed-time convergence and newly develop a strictly intermittent control scheme to stabilize discontinuous systems within a fixed time based on it. The presented method can also be used to effectively estimate the settling time and to simultaneously reveal how the control period, control width, and control gain affect the convergence time of the controlled system. Additionally, we also extend the proposed FxTS method and use it to design a new strictly intermittent control scheme for achieving the preassigned-time stabilization (PaTS) of discontinuous systems. Finally, an example of Chua’s circuit is provided to illustrate the feasibility and applicability of the established FxTS and PaTS methods.

In-memory computing represents an efficient paradigm for high-performance computing using crossbar arrays of emerging nonvolatile devices. While various techniques have emerged to implement Boolean logic in memory, the latency of arithmetic circuits, particularly multipliers, significantly increases with bit-width. In this work, we introduce an in-memory Wallace tree multiplier based on majority gates within voltage-gated spin-orbit torque (SOT) magnetoresistive random access memory (MRAM) crossbar arrays. By utilizing a resistance sum, the majority gate is implemented during READ operations in voltage-gated SOT-MRAM crossbar arrays, resulting in reduced read currents and improved energy efficiency. We employ a series of READ and WRITE operations to perform multiplier calculations, leveraging the fast READ and WRITE speeds of voltage-gated SOT-MRAM devices. Furthermore, the use of five-input majority gates simplifies multiplication by employing uniform logic gates and reducing logic depth, thereby lowering the operation’s complexity and the total number of occupied cells. Our experimental results demonstrate that the proposed in-memory Wallace tree multipliers consume three times less energy for in-memory operations than previously reported$4\times 4$multipliers. Moreover, the proposed method reduces the delay overhead from O ($n^{2}$) to O ($\log _{2}{n}$), where$\mathit {n}$represents the number of bits.

The problem of fixed-time (FXT) and preassigned-time (PAT) optimization is concerned in this article based on multiagent systems (MASs) and power-law algorithms. Under the framework of strong convexity of the cost functions, two types of piecewise algorithms are proposed, which ensure that the FXT optimization can be solved either by first achieving the FXT consensus or by first achieving local optimization. Correspondingly, the PAT optimization problem is also considered by designing several piecewise protocols, where the finished time of optimization can be arbitrary prescribed according to actual demands. Furthermore, these piecewise power-law algorithms on the weighted undirected graphs are generalized to the weighted digraphs. Finally, by providing two numerical examples, the presented algorithms are further verified.

This article focuses on the finite-time stabilization problem for fuzzy spatiotemporal competitive neural networks (FSCNNs) with discrete and distributed delays. First, the differentiable conditions for discrete and finite distributed delays in FSCNNs are removed, and the constraints of the kernel function in infinite distributed delays are weakened. Then, a novel partial differential inequality is proposed to handle the spatial diffusions, which relaxes the restriction for symmetric around the origin of the bounded spatial domain. To stabilize FSCNNs within a finite time, a novel control strategy without delay-dependent terms is established. Moreover, different from the existing works, a more succinct Lyapunov functional is constructed, which does not need to include multiple integral type functional terms to eliminate the influence of the hybrid delays. By virtue of the comparison method and inequality techniques, several sufficient criteria are deduced to guarantee the finite-time stabilization of FSCNNs. Finally, simulations are presented to illustrate the feasibility and effectiveness of the theoretical results.

In this article, the fault detection (FD) filter design problem is addressed for discrete-time memristive neural networks with time delays. When constructing the system model, an event-triggered communication mechanism is investigated to reduce the communication burden and a fault weighting matrix function is adopted to improve the accuracy of the FD filter. Then, based on the Lyapunov functional theory, an augmented Lyapunov functional is constructed. By utilizing the summation inequality approach and the improved reciprocally convex combination method, an FD filter that guarantees the asymptotic stability and the prescribed$H_{\infty }$performance level of the residual system is designed. Finally, numerical simulations are provided to illustrate the effectiveness of the presented results.

This article solves the problems of finite-time control and settling-time estimation for fractional-order quaternion-valued fuzzy neural networks (FQFNNs) with time delays. A novel fractional differential inequality is established to estimate the settling time of the addressed system, which is more general and less conservative than the existing results. In addition, owing to the noncommutativity of multiplication of quaternions, the decomposition method is usually adopted to discuss the finite-time stabilization (FTS) of quaternion-valued neural networks, which inevitably doubles the dimensionality of the system and brings a great computational burden. To avoid the aforementioned issues, some new properties of the quaternion-valued signum function are presented for exploring the FTS of FQFNNs by the direct quaternion method without any decomposition. Then, 1-norm and 2-norm control strategies are designed to stabilize the addressed system in finite time, and several sufficient criteria are derived to ensure the FTS of FQFNNs. Finally, the validity of the obtained theoretical results and the superiority of the proposed estimation method are illustrated by numerical simulations.

In this paper, a unified framework is proposed to address the synchronization problem of memristor chaotic systems (MCSs) via the sliding-mode control method. By employing the presented unified framework, the finite-time and fixed-time synchronization of MCSs can be realized simultaneously. On the one hand, based on the Lyapunov stability and sliding-mode control theories, the finite-/fixed-time synchronization results are obtained. It is proved that the trajectories of error states come near and get to the designed sliding-mode surface, stay on it accordingly and approach the origin in a finite/fixed time. On the other hand, we develop an image encryption algorithm as well as its implementation process to show the application of the synchronization. Finally, the theoretical results and the corresponding image encryption application are carried out by numerical simulations and statistical performances.

This article addresses two kinds of formation tracking problems, namely: 1) the practical formation tracking (PFT) problem and 2) the zero-error formation tracking (ZEFT) problem for multiple Euler-Lagrange systems with input disturbances and unknown models. In these problems, the bounded input constraint, which can be possibly caused by actuator saturation and power limitations, is taken into consideration. Then, the two classes of model-independent distributed control approaches, in which the prior information (i.e., the structures and features) of the system model is not used, are proposed correspondingly. Based on the nonsmooth analysis and Lyapunov stability theory, several novel criteria for achieving PFT and ZEFT of multiple Euler-Lagrange systems are derived. Finally, numerical simulations and comparisons are presented to verify the validity and effectiveness of the proposed control approaches.

In this article, the problems of finite-time/fixed-time synchronization have been investigated for discontinuous neural networks in the unified framework. To achieve the finite-time/fixed-time synchronization, a novel unified integral sliding-mode manifold is introduced, and corresponding unified control strategies are provided; some criteria are established for selecting suitable parameters for solving the related issue, namely, the dynamics of neural network can reach the designed sliding-mode manifold in finite/fixed time, and stay on it thereafter. Moreover, the estimations of setting time are given out. The established unified framework can bring in various protocols by choosing the different parameters of controllers and sliding-mode manifold, which extend previous related results. Finally, some numerical examples are introduced to show the effectiveness and superiority of resulting conclusions.

This article investigates the global exponential stability and stabilization problems for a class of Takagi-Sugeno (T-S) fuzzy competitive neural networks (NNs). In the considered model, we introduce the T-S fuzzy rule to describe the parametric switching causing by complexity and the vagueness in practical environment. Besides, the effects of reaction diffusions and distributed delays, which inherently exist in circuits of NNs, are also taken into consideration. By using the Lyapunov functional theory and Green formula, several stability criteria in terms of \mathbb p-norm are established for the uncompensated fuzzy competitive NNs. Moreover, by designing a fuzzy intermittent controller, the corresponding stabilizability criteria in terms of \mathbb p-norm are derived. We also carry out some discussions and comparisons to further show the less conservativeness and wide applicability of the main theorems. Finally, several examples are presented to verify the obtained results.

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

This paper proposes a unified framework to design sliding-mode control for stabilization of delayed memristive neural networks (DMNNs) with external disturbances. Under the presented framework, finite-time stabilization, and fixed-time stabilization of the controlled DMNNs can be, respectively, obtained by choosing different values for a specific control parameter. It is proved that the system responses can be made reaching the designed sliding-mode surface in finite and fixed time, and then stay on it. Moreover, it also illustrates that the inevitable external disturbances can be rejected by the designed sliding-mode control. Finally, the efficiency and superiority of the obtained main results are verified by comparisons with related works and numerical simulations.

This article investigates the global stabilization problem of Takagi-Sugeno fuzzy memristor-based neural networks with reaction-diffusion terms and distributed time-varying delays. By using the Green formula and proposing fuzzy feedback controllers, several algebraic criteria dependent on the diffusion coefficients are established to guarantee the global exponential stability of the addressed networks. Moreover, a simpler stability criterion is obtained by designing an adaptive fuzzy controller. The results derived in this article are generalized and include some existing ones as special cases. Finally, the validity of the theoretical results is verified by two examples.

This paper investigates the synchronization problem of Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with mixed delays, in which the bounded distributed and unbounded discrete time-varying delays are involved. Then, under the nonsmooth analysis and Lyapunov stability theory, several easily verified algebraic criteria are established to guarantee the global synchronization of FMNNs via a designed fuzzy feedback controller. Moreover, to show the superiority of the theoretical results, several discussions and comparisons with existing work are provided, indicating that derived results in this paper are general and include several existing ones as special cases. Finally, two numerical examples and two applications in psuedorandom number generation and image encryption are presented to show the validity and practicability of the theoretical results.

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

This paper is concerned about the finite-time stabilizability and instabilizability for a class of delayed memristive neural networks (DMNNs). Through the design of a new nonlinear controller, algebraic criteria based on M -matrix are established for the finite-time stabilizability of DMNNs, and the upper bound of the settling time for stabilization is estimated. In addition, finite-time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller. The effectiveness and the superiority of the obtained results are supported by numerical simulations.

In this paper, adaptive synchronization of memristor-based neural networks (MNNs) with time-varying delays is investigated. The dynamical analysis here employs results from the theory of differential equations with discontinuous right-hand sides as introduced by Filippov. Sufficient conditions for the global synchronization of MNNs are established with a general adaptive controller. The update gain of the controller can be adjusted to control the synchronization speed. The obtained results complement and improve the previously known results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.