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In this paper, the almost periodic dynamical behaviors are considered for delayed complex-valued neural networks with discontinuous activation functions. We decomposed complex-valued to real and imaginary parts, and set an equivalent discontinuous right-hand equation. Depended on the differential inclusions theory, diagonal dominant principle, non-smooth analysis theory and generalized Lyapunov function, sufficient criteria are obtained for the existence uniqueness and global stability of almost periodic solution of the equivalent delayed differential system. Especially, we derive a series of results on the equivalent neural networks with discontinuous activations and periodic coefficients or constant coefficients, respectively. Finally, we give one numerical example to demonstrate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

• As a first attempt, the SMC problem of PDT switched nonlinear systems is addressed, and the dynamic ET mechanism is introduced to alleviate the limited bandwidth resources, which is more general. • With the dynamic ET mechanism, a new switched SMC law is constructed with the PDT switching strategy that is more general than DT and ADT switching strategies, which can match the subsystem one by one more reasonably and reduce the conservativeness to some extent. • Based on the Lyapunov function approach, some sufficient conditions, which can ensure both the reachability and globally uniform exponential stability with an H ∞ performance of the closed-loop PDT switched system, are derived. In this paper, the H ∞ sliding mode control problem of persistent dwell-time switched nonlinear systems is investigated. Due to the limited bandwidth resources, a dynamic event-triggered mechanism is introduced to alleviate the transmission burden. Considering that the system parameters are switched in accordance with the persistent dwell-time switching strategy, a novel switched sliding mode control law is constructed. Then, drawing on the Lyapunov function approach, sufficient conditions are derived, which not only ensure the reachability of the sliding region around the specified sliding surface but also guarantee the globally uniform exponential stability of the system with an H ∞ performance. Moreover, the specific form of the controller gains is derived by utilizing an efficient decoupling method. Eventually, the validity of the proposed method is validated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies the discrete-time slow state feedback fault-tolerant controller design issue for Takagi-Sugeno fuzzy-model-based Markov jump singularly perturbed nonlinear systems, in which transition probabilities of systems subject to persistent dwell-time switching mechanism. In order to eliminate the influence of actuator faults and provide a more flexible control strategy, a multi-objective fault-tolerant controller is designed to ensure the stability of the system and meet the requirements of various performance indexes. The goal is to establish some sufficient conditions, which ensure the mean-square exponential stability and the extended dissipativity performance of the closed-loop system. Furthermore, the gains of the designed controller can be obtained by solving the problem of convex optimization. Finally, the availability of the designed controller is demonstrated by a numerical example and a tunnel diode circuit system. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the dynamic behavior of periodic solution for the high-order discrete-time Cohen–Grossberg neural networks (CGNNs) with time delays. First, the existence is studied based on the continuation theorem of coincidence degree theory and Young’s inequality. And then, the criterion for the global exponential stability is given using Lyapunov method. Finally, simulation result shows the effectiveness of our proposed criterion. [ABSTRACT FROM AUTHOR]

• As the first attempt, we considered the state information required by the sliding mode controller will be randomly dropouts, which is reflected in the obtained equivalent sliding mode controller. • A novel method is utilized for the SMC problem of the PDT switched systems with data dropouts, and a novel SMC law is proposed. • For the PDT switched systems, some sufficient conditions to guarantee the mean-square exponential stability with data dropouts are derived for the PDT switched systems and the H ∞ performance of the system is analyzed through utilizing the linear matrix inequality technique. This paper concentrates on the sliding mode control problem for a set of discrete-time switched systems. As the first attempt, the persistent dwell-time switching rule is considered in the research of sliding mode control for switched systems. Furthermore, data dropouts are frequently encountered in the process of data transmission, and it should be considered in the process of designing the sliding mode control law so that the state trajectories are guaranteed to move in a region around the specified sliding surface. Based on the Lyapunov theory and the matrix convex optimization technique, the main concern of this paper is to construct a sliding mode controller to ensure that the closed-loop system is mean-square exponentially stable with a prescribed weighted H ∞ performance. Finally, the effectiveness and rationality of the obtained results are verified by a numerical example. [ABSTRACT FROM AUTHOR]

• The mean square exponential stability of high-order Markovian jump reaction-diffusion. • HNNs (RHNNs) with GUTRs is firstly discussed. • The uncertainties exist in not only parameters but also transition rates. • Each transition rate can be completely unknown or only its estimate value is known. • Our models are more comprehensive and some existing results are special cases of ours. • A numerical example illustrates the validity of our findings. This paper focuses on mean square exponential stability of high-order Markovian jump reaction-diffusion HNNs (RHNNs) with uncertain transition rates (GUTRs) and time-varying delays by Lyapunov-Krasovskii functional method and linear matrix inequality (LMI). In this GUTR model, only part of the transition rates can be known, namely, its estimate error and estimate value are known, but the others have no useful information. Our models are more comprehensive and some existing results are special cases of ours. Finally, a numerical example illustrates the validity of our findings. [ABSTRACT FROM AUTHOR]