The slow state variables feedback stabilization problem for semi-Markov jump discrete-time systems with slow sampling singular perturbations is discussed in this work. A new fairly comprehensive system model, semi-Markov jump system with singular perturbations, which is more general than Markov jump model, is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems. Based on a slow state variables feedback control scheme, a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated. With the help of the discrete-time semi-Markov kernel approach, some sojourn-time-dependent and less-conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed. Finally, an illustrative example is given to show the superiority and usefulness of the proposed method.

This paper investigates the finite-time event-triggered $\mathcal{H}_\infty$ control problem for Takagi-Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this work is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closed-loop system is finite-time bounded and satisfies a prescribed $\mathcal{H}_\infty$ performance level, but also the communication burden is reduced. Firstly, a sufficient condition is established for the finite-time bounded $\mathcal{H}_\infty$ performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the method of the desired controller design is presented. Two illustrative examples are finally presented to demonstrate the practicability and efficacy of the proposed method.

This paper researches the fuzzy-model-based non-fragile control problem for nonlinear discrete-time singularly perturbed systems with Markov jumping parameters. To remove the restriction of sojourn-time in widely used discrete-time Markov jump model, i.e. the sojourn-time is subject to a geometric distribution which leads that the transition probabilities is memoryless, the semi-Markov jump model in which the ${memory}$ property of the transition probabilities is considered, is adopted to describe the stochastic jump parameters in the nonlinear singularly perturbed systems. Based on the T-S fuzzy model approach and semi-Markov Kernel concept, several criteria ensuring $\delta$-error mean square stability of the underlying closed-loop system are established. With the help of those criteria, the design procedures of a resilient controller which can well deal with the fragility problem in the implementation of the proposed fuzzy-model-based controller is presented and a technique is developed to estimate the larger permissible maximum value of singularly perturbed parameter for discrete-time nonlinear semi-Markov jump singularly perturbed systems. Finally, the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit.

This article investigates the reliable output feedback control problem for networked nonlinear semi-Markov jump systems, in which a control strategy with redundant channels is established to reduce the adverse effect caused by packet dropouts. The actuator faults are fully considered in the setup. On the basis of stochastic analysis theory and fuzzy-model-based method, some criteria are established to guarantee the σ-error mean-square stability for the considered systems. As a consequence, the reliable output feedback controller design method is proposed, which can be utilized to deal with the actuator failures problem effectively. Finally, two illustrative examples are employed to explain the availability of the presented design approach, where the single-link robot arm system model is contained.