This paper is concerned with the state estimation and sliding-mode control problems for continuous-time Markovian jump singular systems with unmeasured states. Firstly, a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic admissibility of the unforced Markovian jump singular system. Then, the sliding-mode control problem is considered by designing an integral sliding surface function. An observer is designed to estimate the system states, and a sliding-mode control scheme is synthesized for the reaching motion based on the state estimates. It is shown that the sliding mode in the estimation space can be attained in a finite time. Some conditions for the stochastic admissibility of the overall closed-loop system are derived. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

This paper investigates the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. Based on a novel fuzzy Lyapunov-Krasovskii functional, a delay partitioning method has been developed for the delay-dependent stability analysis of fuzzy time-varying state delay systems. As a result of the novel idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. A delay-dependent stabilization approach based on a nonparallel distributed compensation scheme is given for the closed-loop fuzzy systems. The proposed stability and stabilization conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved readily by using existing LMI optimization techniques. Finally, two illustrative examples are provided to demonstrate the effectiveness of the techniques proposed in this paper.

This technical brief is concerned with dissipativity analysis and dissipativity-based sliding mode control (SMC) of continuous-time switched stochastic systems. Firstly, a sufficient condition is proposed to guarantee the mean-square exponential stability and strict dissipativity for the switched stochastic system. Then, an integral-type sliding surface function is designed for establishing a sliding mode dynamics, which can be formulated by a switched stochastic system with an external disturbance/uncertainty. Dissipativity analysis and synthesis are both investigated for the sliding mode dynamics, and consequently sufficient conditions are derived, which pave the way for solving the dissipativity analysis and control problems. Moreover, a SMC law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time. Finally, the efficiency of the theoretical findings is demonstrated by an illustrative example.