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In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov–Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available. [ABSTRACT FROM AUTHOR]

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of output feedback control for a class of continuous-time hidden semi-Markov jump systems with time delays. Due to the limitations of the actual environment, system modes are usually undetectable, which are called hidden modes. The controller modes are described as observable modes. Emission probabilities are used to establish the relationship between abovementioned two concepts. The jump parameters are governed by the hidden semi-Markov process, which can better describe the asynchronous information between the controller modes and the system modes. Besides, time delays are considered to be time-varying and dependent on the hidden modes. By employing some mathematical transformation and constructing a novel Lyapunov–Krasovskii functional, some new parameter-dependent sufficient stabilization conditions can be obtained by designing an observed-mode-dependent static output-feedback controller. Finally, a practical example is provided to illustrate the effectiveness and merits of the proposed methods. [ABSTRACT FROM AUTHOR]