This article develops a novel event-triggered finite-time control strategy to investigate the finite-time synchronization (F-tS) of fractional-order memristive neural networks with state-based switching fuzzy terms. A key distinction of this approach, compared with existing event-based finite-time control schemes, is the linearity of the measurement error function in the event-triggering mechanism (ETM). The advantage of linear measurement error not only simplifies computational tasks but also aids in demonstrating the exclusion of Zeno behavior for fractional-order systems (FSs). Furthermore, to derive F-tS criteria in the form of linear matrix inequalities (LMIs), a novel finite-time analytical framework for FSs is proposed. This framework includes two original inequalities and a weighted-norm-based Lyapunov function. The effectiveness and superiority of the theoretical results are demonstrated through two examples. Both theoretical and experimental results suggest that the criteria obtained using the new analytical framework are less conservative than existing results.

Considering the memory property of the fractional calculus and the potential diverging state of the open-loop mode, existing analysis methods are difficult to solve the finite-time issue of intermittently controlled fractional-order systems (FOSs). This article studies the finite-time synchronization of coupled FOSs with nonlinearity via fuzzy intermittent quantized control and two novel fractional-order differential inequalities. An interval-type 2 Takagi–Sugeno fuzzy technique is introduced, which not only facilitates the handling of the nonlinear term in the error dynamic system, but also greatly simplifies the control design. Synchronization conditions in form of linear matrix inequalities are provided by designing a novel Lyapunov function on the basis of ellipsoidal norm. Moreover, two corollaries show the generality of the new analysis framework. Compared with existing results, it is amazing that the decreasing magnitude of Lyapunov function on the control intervals can be smaller than its increasing magnitude on the subsequent noncontrol interval. Finally, Chua’s system is used to clarify the effectiveness of theoretical outcomes.

This article focuses on finite-time$\mathcal {L}_{2}$stabilization of T–S fuzzy systems with time delays and parameter uncertainties via intermittent control. To cope with the effects of parameters uncertainties, time delays, and intermittent divergence simultaneously, a new finite-time stability lemma for intermittently controlled systems is presented. Then, a weighted 2-norm Lyapunov–Krasovskii functional (LKF) is established, which has the advantage that it is convenient to derive less conservative linear matrix inequality sufficient conditions and to overcome the difficulty in analyzing$\mathcal {L}_{2}$performance under intermittent control frameworks. Another advantage of our result over existing results is that the growth increment of the LKF on the noncontrolled interval can be larger than the decreasing magnitude on the controlled interval. The merits of the theoretical results are examined by a numerical example and a coupled Chua's circuit.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov-Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.

It is challenging to deal with the relationship between the triggering interval and the dwell time when mode-pendent event-triggered control is considered for switched systems, especially complete actuator faults occur in some subsystems (or modes). Therefore, this article considers the exponential stabilization almost surely (ES a.s.) for a class of Takagi–Sugeno fuzzy systems with delay and stochastic switching by designing a novel mode-dependent event-triggered output control. It is assumed that only the measured output can be utilized in designing the controller and complete actuator faults occur in some modes. Periodic sampling is utilized to avoid the Zeno phenomenon. Combining the sampling interval with delay-partitioning method, a fuzzy Lyapunov–Krasovskii functional (LKF) is designed on the basis of the derivative of the membership functions to obtain less conservative results. Especially, the increment coefficient of the multiple LKF at switching instant is smaller than one. The maximum feasible value of the sampling interval is derived and the control gains are designed by solving linear matrix inequalities. Our results show that the ES a.s. is ensured though some modes are not controlled. Numerical simulations demonstrate the merits of the theoretical analysis. It is significant to find by numerical simulations that the time delay cannot be divided into too small values though the delay-partitioning method is effective in reducing the conservativeness.

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction by solving the$L_{1}$-minimization problem. First, two centralized neurodynamic approaches are designed based on the augmented Lagrange method and the Lagrange method with derivative feedback and projection operator. Then, the optimality and global convergence of them are derived. In addition, considering that the collective neurodynamic approaches have the function of information protection and distributed information processing, first, under mild conditions, we transform the$L_{1}$-minimization problem into two network optimization problems. Later, two collective neurodynamic approaches based on the above centralized neurodynamic approaches and multiagent consensus theory are proposed to address the obtained network optimization problems. As far as we know, this is the first attempt to use the collective neurodynamic approaches to deal with the$L_{1}$-minimization problem in a distributed manner. Finally, several comparative experiments on sparse signal and image reconstruction demonstrate that our proposed centralized and collective neurodynamic approaches are efficient and effective.

This article considers the stabilization issue of switched discrete-time positive systems (SDPSs) with delay by using asynchronous control. Combining transition probability (TP) with mode-dependent average dwell time (MDADT), called TP-based MDADT switching, the SDPSs are more practical than classical models with average dwell-time (ADT) switching. With the aid of a co-positive Lyapunov–Krasovskii functional (CLKF), sufficient conditions ensuring the exponential stability almost surely (ES a.s.) of the SDPSs without control is studied, where the mode is not necessary to be stable. After that, a mode-dependent controller with switching delay is designed to stabilize the SDPSs in the case that there are unstable subsystems. An algorithm is provided to design the control gains. It is discovered that the mode in the closed-loop SDPSs is not required to be stable on synchronous and asynchronous switching intervals. Numerical simulations verify the merits of the new results.