State estimation and Sliding-Mode Control of Markovian Jump Singular Systems

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