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

• Published in: IEEE transactions on automatic control Vol. 55; no. 5; pp. 1213 - 1219
• Main Authors: Wu, Ligang, Shi, Peng, Gao, Huijun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Applied sciences; Automatic control; Computer science; control theory; systems; Control system analysis; Control systems; Control theory. Systems; Convergence; Distributed algorithms; Estimates; Exact sciences and technology; H infinity control; Markovian jump; Mathematical analysis; Modelling and identification; Motion estimation; observer; Observers; singular systems; Sliding mode; Sliding mode control; State estimation; Stochastic systems; Stochasticity; Terrain factors; unmeasured states; Wireless sensor networks; Markov process; Singularity; singular systems; sliding-mode control; Admissibility; Markovian system; Probabilistic approach; Variable structure control; Necessary and sufficient condition; Sliding mode; Variable structure system; Continuous time; Closed feedback; unmeasured states; Observer; Linear matrix inequality; Jump process; System identification; Jumping; State estimation; Markovian jump
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2042234

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.