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

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3 Author(s)
Ligang Wu ; Space Control & Inertial Technol. Res. Center, Harbin Inst. of Technol., Harbin, China ; Peng Shi ; Huijun Gao

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 5 )