Controlling discrete-time linear systems with unknown model information while reducing control costs poses considerable obstacles. To tackle this issue, this paper proposes two novel data-driven impulsive control (IMC) frameworks for discrete-time linear systems. First, unlike most existing IMC strategies that rely on accurate system models or system identification, the proposed methods can directly design controllers based on measured data. Moreover, for data-driven IMC schemes that respect the average impulsive interval, the exponential stabilization of the system is demonstrated under the strong rank condition by leveraging relevant data and invoking the concepts of Lyapunov functions and the iterative synthesis procedure. Second, to reduce unnecessary impulsive actions during information transmission and thereby enhance control performance, a data-driven event-triggered impulsive control (ETIMC) approach is examined by combining event-triggered control with IMC. To mitigate the requirement for persistent excitation of input data, the concept of data informativity is utilized for analysis, and sufficient criteria for system stabilization under the proposed data-driven ETIMC are established in conjunction with the collected data. Ultimately, the validity of the theoretical results is verified through two illustrative examples.

The practically fixed-time leaderless cluster synchronization is addressed for uncertain spatiotemporal networks (USTNs) with coopetition interactions, actuator faults and external disturbances. Firstly, by introducing sign-based coupling, a class of USTN is formulated to capture the dynamics of coopetition interactions among different clusters, which provides a more accurate representation compared to dynamical networks with unsigned coupling. Secondly, a practical fixed-time (PFT) convergence theorem is developed for a general partial differential system, which relaxes the constraints on the derivative of the Lyapunov function and provides a less conservative method for estimating the settling time. Subsequently, a distributed fault-tolerant control algorithm is designed to drive the cluster synchronization error to an adjustable attraction region in a fixed time. By exploring specific properties of the intra-cluster Laplacian matrix and proposing a new inter-degree balanced condition, several flexible synchronization criteria are derived and a quantitative relationship among control parameters, the settling time and the size of the attraction region is presented. Finally, the effectiveness of the developed controllers and criteria is validated through a coupled reaction-diffusion neural network.

While control barrier functions (CBFs) are capable of providing safety guarantees, their effectiveness can degrade in the presence of model uncertainty and unexpected faults, particularly under actuator gain faults. To deal with these challenges, this paper proposes a probabilistically safe and adaptive control framework that integrates Gaussian processes (GPs) and online fault estimation into CBF-/high-order CBF-based methods. To handle the influence of model uncertainty, we leverage GP regression for the construction of CBFs, high-order CBFs, and an online estimator. In addition, the GP-based online estimator to estimate unknown actuator gain faults. Finally, two numerical examples are provided to validate two CBF-based methods and to demonstrate the effectiveness and superiority of these methods in ensuring safety compared to existing approaches.

This article investigates quasi-projective synchronization (Q-PS) of discrete-time fractional-order delayed memristive neural networks (DFDMNNs) with uncertainties. Firstly, by virtue of some useful inequality skills and basic properties of discrete-time fractional calculus as well as fixed-point theorem, several sufficient criteria on the existence of solutions for DFDMNNs with uncertainties are derived. Furthermore, Q-PS of DFDMNNs is explored under the delayed state feedback controller, and corresponding Q-PS criteria are established. Finally, one numerical example is presented to verify the availability of the theoretical results.

This article focuses on the fixed-time (FXT) and preassigned-time (PAT) bipartite output regulation of heterogeneous linear multiagent systems (MASs), where both cooperative and adversarial interactions among neighboring agents are considered under a signed graph framework. Since the exosystem information may be unavailable to the agents, an FXT distributed observer and an FXT adaptive distributed observer are designed to accurately identify the exosystem's coefficient matrix and state, respectively. Subsequently, in the absence of the stabilizability and detectability of coefficient matrices, distributed state- and output-feedback control protocols are designed to ensure FXT bipartite output regulation. Besides, for a preset convergence time, the bipartite output regulation is explored by developing control protocols incorporating distributed PAT observers and controllers. Finally, the theoretical results are applied to warehouse automation robot systems.

This article focuses on the bipartite output synchronization for a type of fuzzy fractional output-coupled networks based on fractional-order fuzzy adaptive strategies. Firstly, in view of the unavailability of state information caused by irresistible factors and the coexistence of cooperative and competitive relations in reality, a class of T-S fuzzy fractional networks with output couplings is established under the signed graph framework. Next, a type of membership function-dependent fractional adaptive schemes is presented to automatically regulate the control gains, some criteria of bipartite output synchronization are derived based on the characteristic of the signed topology instead of traditional gauge transformation method. Particularly, a pinning adaptive control scheme is employed to investigate bipartite output synchronization for fuzzy fractional output-coupled networks with the positive-definite output matrix, which determines the pinning nodes just dependent of the cooperative links among nodes in signed graph. The developed criteria are finally confirmed by some examples.

In this paper, the fixed-time intra/inter-layer output synchronization problem of output-coupled multiplex networks is investigated utilizing a dynamic event-triggered control method. Firstly, to solve the issue of unavailability of node states resulting from uncontrollable factors, a multiplex networks model with observable intra/inter-layer output coupling information is constructed. Subsequently, two dynamic event-triggered control strategies based on output information are proposed, on the basis of which the fixed-time output synchronization criteria are established and Zeno behavior is excluded. The controllers proposed in this paper replace the common linear terms and multiple power-law terms in the existing fixed-time controllers with an exponential term based on the output errors, and also no longer include the intra/inter-layer coupling information of the nodes, making the form of the controllers more streamlined and easier to implement the control strategies. Finally, the effectiveness of the designed control protocols is verified by some numerical simulations based on Chua’s circuit as well as spacecraft formation control.

This article addresses the fixed-time leaderless cluster synchronization of spatiotemporal community networks (SCNs) characterized by nonidentical node dynamics and reaction-diffusion feature. First, a signed SCN with reaction-diffusion effect is formulated, where the sign-based coupling is introduced to capture the dynamics of coopetition interactions among different communities. Second, to ensure the invariance of the synchronous manifold, an improved interdegree balance condition is proposed as a prerequisite for achieving cluster synchronization of the community network. Third, based on the local state information from adjacent nodes within each community, a time-limited controller is designed to enhance intracommunity coordination while avoiding the adverse effects of intercommunity competition on synchronization. Subsequently, with the help of the matrix decomposition technique and a Lyapunov-like method, several flexible leaderless cluster synchronization criteria are derived by establishing a nontrivial integral inequality and key properties of the intracommunity Laplacian matrix. Finally, the theoretical results are substantiated through a numerical example.

Fault-tolerant control (FTC) is an effective control method designed to maintain a faulty system within an acceptable risk level while ensuring its safety. However, handling both uncertainties and faults in a system remains challenging. In this article, we propose two probabilistic model-based adaptive FTC methods for faulty nonlinear systems with unknown dynamics. We study Gaussian process (GP) regression in two cases: 1) an offline learning-based control method and 2) an event-triggered online data-driven modeling method, to learn unknown system dynamics. Considering the computational complexity of GP regression in practical applications, we discuss the case of computational delays in real-time predictions. Moreover, we develop four theoretical criteria to ensure the probabilistic stability of closed-loop systems. Finally, numerical simulations validate the effectiveness of proposed control methods and demonstrate their competitiveness compared to existing approaches.

This article is committed to studying projective synchronization and complete synchronization (CS) issues for one kind of discrete-time variable-order fractional neural networks (DVFNNs) with time-varying delays. First, two new variable-order fractional (VF) inequalities are built by relying on nabla Laplace transform and some properties of Mittag-Leffler function, which are extensions of constant-order fractional (CF) inequalities. Moreover, the VF Halanay inequality in discrete-time sense is strictly proved. Subsequently, some sufficient projective synchronization and CS criteria are derived by virtue of VF inequalities and hybrid controllers. Finally, we exploit numerical simulation examples to verify the validity of the derived results, and a practical application of the obtained results in image encryption is also discussed.

This article is dedicated to an investigation of state estimation for discrete-time fractional-order nonautonomous neural networks (DFNNNs) with leakage and discrete delays. To this end, some inequalities with more free parameters are obtained based on results related to nabla fractional difference, which considerably extend the existing results. In light of the effective estimator, some sufficient conditions to ensure the global asymptotic stability of the error system are obtained to solve the state estimation problem for DFNNNs by means of the linear matrix inequality (LMI) and the established inequalities. Finally, the theoretical results are verified by numerical simulations.

This article presents two fixed-time (FXT) distributed adaptive algorithms to solve a class of convex optimization problems for multiagent systems. First, a distributed adaptive protocol based on edge weights is developed to achieve global FXT optimization, in which the initial states are the local optimal points. Subsequently, an adaptive power-law algorithm is designed to realize local FXT optimization for each agent with arbitrary initial state. In the convergence analysis, unlike previous analysis method based on Lyapunov FXT stability criteria, this study employs the definition of FXT stability with Laplace transformation and a method of contradiction, several sufficient conditions are obtained to ensure that the states of all agents converge to the global optimal value within a fixed time, and the upper bound of convergence time is estimated. Furthermore, these adaptive algorithms on undirected graphs are extended to weight-balanced digraphs. Finally, the validity of the proposed edge-based adaptive distributed algorithms is demonstrated through numerical simulations of two packet-level charge-state balance problems.

Recently, gauge transformation-based bipartite synchronization has received much interest, but the method of gauge transformation alters the original signed topological structure and the competition or cooperation among individuals is obscured. In addition, the heterogeneity of nodes brings great difficulty and challenge for heterogeneous networks to achieve complete synchronization like homogeneous networks. In this article, without converting signed graph into corresponding unsigned structure via the gauge transformation, the bipartite complete synchronization of heterogeneous fractional networks is explored. Above all, a mathematic model of fractional networks with signed topology and heterogeneous nodes’ dynamics is introduced, in which the topological graph possesses both negative and positive edges to illustrate the competition and cooperation between individuals, and the desired synchronized state is an arbitrarily specified smooth orbit and not necessarily the decoupled state. Additionally, two innovative control schemes with logarithmic quantizer are developed, and several conditions are obtained to reach bipartite complete synchronization of fractional heterogeneous networks just by virtue of the Laplacian matrix of the original signed graph rather than the traditional technique of gauge transformation. The theoretical analysis is eventually confirmed by several numerical results.

This article is concerned about fixed-time (FT) synchronization of spatiotemporal networks (STNs) with the Robin boundary condition. Above all, a switching-type FT stability theorem and an integral inequality are established, which provide a novel theoretical tool for the rigorous analysis of FT control in STNs. Subsequently, three kinds of nontrivial power-law controllers are developed which are separately acted on the interior, the boundary, and the whole of the spatial domain. Based on these control schemes and Lyapunov-like method, several flexible criteria are obtained to achieve FT synchronization of STNs, and the upper bound of the synchronization time is explicitly estimated. Note that, the derived results here are also perfectly applicable to STNs with Neumann or Dirichlet boundary condition. Several illustrate examples are presented at final to confirm the developed controllers and criteria.

This article studies synchronization issues for a class of discrete-time fractional-order quaternion-valued uncertain neural networks (DFQUNNs) using nonseparation method. First, based on the theory of discrete-time fractional calculus and quaternion properties, two equalities on the nabla Laplace transform and nabla sum are strictly proved, whereafter three Caputo difference inequalities are rigorously demonstrated. Next, based on our established inequalities and equalities, some simple and verifiable quasi-synchronization criteria are derived under the quaternion-valued nonlinear controller, and complete synchronization is achieved using quaternion-valued adaptive controller. Finally, numerical simulations are presented to substantiate the validity of derived results.

This article studies a distributed Nash equilibrium (NE) seeking problem for multiple agents of aggregative games. A novel distributed algorithm is presented to assure both fast convergence and nonovershoot performance by the combination of an accelerated method and a gradient-based NE seeking algorithm. To be specific, an accelerated method (i.e., the heavy-ball method or Nesterov’s accelerated method) is introduced in the designed algorithm for the fast convergence of agents’ strategies to the NE. Moreover, a suitable switching mechanism is proposed to improve the transient performance by switching the distributed algorithm based on the accelerated method to the gradient-based algorithm. As a result, the presented distributed algorithm is modeled by a hybrid dynamical system (HDS). The semi-globally practical convergence is established by analyzing the stability of a parameterized HDS. An example of distributed energy resources is taken to verify the presented algorithm.

This article aims to study the fixed-time (FxT) synchronization of different dimensional Filippov systems. New FxT stability lemmas containing the classical inequality$\dot {V}\leq {-c}_{1}V^{a}-c_{2}V^{b}$proposed by Polyakov are established. Different from the previous FxT stability lemmas in the literature, the proposed one shows the new conclusion that the settling times can be larger or smaller as long as$c_{1}$and$c_{2}$satisfy the certain relationships, which synchronously reveals that the relationships between the control gains can lead to different settling times. Besides, a generalized economical inequality condition$\dot {V} \leq -c_{1}V-c_{2}V^{\upsilon +{\mathrm{ sign}}(V-r)}$is proposed and a novel FxT stability lemma is also established. The complete theoretical proof is given to reveal that$r=1$leads to desired settling time, some previous related results are improved. Based on the new FxT stability lemmas and differential inclusion theory, algebraic inequality conditions are provided to guarantee the FxT synchronization, which reports the first result on the FxT synchronization of different dimensional Filippov systems. Finally, numerical examples are provided to verify the correctness of the main theoretical results.

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 proposes fixed-time stability lemmas for the Filippov system via some new inequality approaches. The adopted method no longer needs to integrate the Lyapunov function$V$on the two integral intervals, which is quite different from the existing ones. Some new estimations of the settling times are provided. Also, the steepness exponents of the Lyapunov function$V$in the previous fixed-time stability lemmas are improved. In order to further study the nondifferentiable delayed neural networks modeled by the Filippov system, a class of discontinuous uncertain Cohen–Grossberg neural networks (CGNNs) with mixed delays is formulated and the distributed delays are nondifferentiable, which is more general. Due to the existence of nondifferentiable distributed delays, the existence of the periodic solutions is proved by Kakutani’s fixed-point theorem before considering the stability. By virtue of the obtained fixed-time stability lemmas and the constructed delay-product-type Lyapunov–Krasovskii functional, the fixed-time stabilization is obtained via a no-chattering controller. Clearly, the designed controller does not contain integral terms and delay terms for dealing with the time delays in the closed-loop system, which is more simplified and practical. Finally, two examples help examine the correctness of the main results.

In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p-norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results.

This article studies the$H_{\infty }$exponential synchronization problem for complex networks with quantized control input. An aperiodic sampled-data-based event-triggered scheme is introduced to reduce the network workload. Based on the discrete-time Lyapunov theorem, a new method is adopted to solve the sampled-data problem. In view of the aforementioned method, several sufficient conditions to ensure the$H_{\infty }$exponential synchronization are acquired. Numerical simulations show that the proposed control schemes can significantly reduce the amount of transmitted signals while preserving the desired system performance.

Fixed-time stability (FXTS) and fixed-time control (FXTC) of dynamic systems are reconsidered in this article based on special functions from the view of improving the estimate accuracy of settling time (ST) and reducing the chattering caused by the sign function. First, by means of the idea of contradiction and variable transformations, some generic FXTS criteria are established and some upper bounds of ST are directly calculated and expressed by several special functions. It is further proved that these estimates are the most accurate compared with the existing results. Besides, to suppress the chattering caused by the sign function, some saturation functions are constructed to replace the sign function and the FXTS of the new system obtained by replacing is ensured by rigorous theoretical analysis. As applications, the problem of stabilization for chaotic systems in fixed or preassigned time is explored. Especially, an innovative saturation controller is developed to realize preassigned-time stabilization, where the convergence time is prescribed in advance according to actual requirement and the control gains are finite, the existing control methods with time-varying infinite gains are essentially improved. Lastly, three numerical examples are provided to verify the improved estimates of ST and the chattering reduction.

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 mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.

This article is concerned with the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks by improving FXT stability and developing simple control schemes. First, some more relaxed conditions for FXT stability are established and several more accurate estimates for the settling time (ST) are obtained by means of some special functions. Based on the improved FXT stability, FXT synchronization for discontinuous networks is discussed by designing a simple controller without a linear feedback term. Besides, the PAT synchronization is also explored by developing several nontrivial control protocols with finite control gains, where the synchronized time can be prespecified according to actual needs and is irrelevant with any initial value and any parameter. Finally, the improved FXT stability and the synchronization for complex networks are confirmed by two numerical examples.

In this paper, without dividing complex-variable networks into two subsystems with real values, the finite-time synchronization is considered for complex-valued dynamical networks with fractional order by means of the theory of complex-variable functions. First of all, as a generalization of the real-valued sign function, the sign functions of complex-valued numbers and complex-valued vectors are introduced and some formulas about them are established. Under the sign function framework, two complex-valued control strategies are designed based on two different norms of complex numbers. Some synchronization criteria are derived and the settling times of synchronization are effectively estimated by developing fractional-order finite-time differential inequalities and utilizing the theory of complex-variable functions. The established theoretical results are demonstrated and the effect of the fractional order of the network model on the finite-time synchronization is revealed finally by providing some numerical simulations.

In this paper, the problem of the finite-time synchronization is addressed for a kind of fractional-order memristive neural networks (FMNNs). First, a new power law inequality with fractional-order and two finite-time fractional differential inequalities are established by means of L'Hospital rule, Laplace transform, and reduction to absurdity, which greatly extend some existing results. In addition, unlike the traditional maximum absolute value-based method to propose memristive synaptic weights, by introducing some transformations, FMNNs are translated to a type of fractional-order systems with uncertain parameters. Furthermore, the finite-time synchronization of FMNNs is investigated by designing a discontinuous control scheme and several criteria are derived based on the developed fractional inequalities and M-matrix theory. Note that in addition to the traditional Lyapunov function with absolute value form, a more general Lyapunov function is constructed to deal with the finite-time synchronization, which makes the derived criteria more flexible and less conservative. Lastly, the derived theoretical results are verified via numerical simulations.

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.

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 exponential stability of fractional-order impulsive control systems (FICSs) and exponential synchronization of fractional-order Cohen-Grossberg neural networks (FCGNNs). First, under the framework of the generalized Caputo fractional-order derivative, some new results for fractional-order calculus are established by mainly using L'Hospital's rule and Laplace transform. Besides, FICSs are translated into impulsive differential equations with fractional-order via utilizing the definition of Dirac function, which reveals that the effect of impulsive control on fractional systems is dependent of the order of the addressed systems. Furthermore, exponential stability of FICSs is proposed and some novel criteria are obtained by applying average impulsive interval and the method of induction. As an application of the stability for FICSs, exponential synchronization of FCGNNs is considered and several synchronization conditions are established under impulsive control. Finally, several numerical examples are provided to illustrate the effectiveness of the derived results.

In this paper, a periodic intermittent sampled data control strategy, which both reduces the load of updating rate of the controller and cuts down the working time of the controller in each sampling interval, is proposed to investigate the second-order consensus of multiagent systems. In order to reach consensus, a necessary and sufficient condition depending on the coupling gains, the communication width, the sampling period, and the spectrum of the Laplacian matrix, is established. Furthermore, the feasible region of communication width is derived for given coupling gains and structure of network. Besides, the coupling gains are also carefully designed. On the other hand, when the time delay exists in the sampling process, a time delayed protocol is proposed. A necessary and sufficient condition based on the communication width, the sampling period, the coupling gains, the time delay, and the network structure is also derived for achieving consensus. It is amazing found that the sampling period should have both lower and upper bounds for given time delay and communication width for the sake of reaching consensus. Finally, several numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 <; α <; 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.

In this paper, the exponential synchronization for a class of complex networks with finite distributed delays coupling is studied via periodically intermittent control. Some novel and useful criteria are derived by utilizing a different technique compared with some correspondingly previous results. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural networks with distributed delays are obtained. Furthermore, a feasible region of the control parameters is derived for the realization of exponential synchronization. It is worth noting that the synchronized state in this paper is not an isolated node but a non-decoupled state, in which the inner coupling matrix and the degree of the nodes play a central role. Additionally, the traditional assumptions on control width, non-control width, and discrete delays are removed in our results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control method.

This paper discuss the global exponential stability and synchronization of the delayed reaction-diffusion neural networks with Dirichlet boundary conditions under the impulsive control in terms of p-norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction-diffusion neural networks with Dirichlet boundary conditions. Some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed control methods.