Sliding mode control of singular stochastic hybrid systems

• Published in: Automatica (Oxford) Vol. 46; no. 4; pp. 779 - 783
• Main Authors: Wu, Ligang, Ho, Daniel W.C.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.04.2010; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Disturbances; Dynamical systems; Dynamics; Exact sciences and technology; Markovian jump systems; Sheet molding compounds; Singular systems; Sliding mode; Sliding mode control; Sliding mode control (SMC); Stochastic systems; Stochasticity; Markovian jump systems; Sliding mode control (SMC); Stochastic systems; Singular systems; Markov process; Multimodel control; Singularity; Markovian system; Variable structure control; Sliding mode; Non linear control; Stochastic stability; Non linear system; Hybrid system; Uncertain system; Linear matrix inequality; Jump process; Jumping; Non deterministic system
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.01.010

This paper is concerned with the sliding mode control (SMC) of nonlinear singular stochastic systems with Markovian switching. An integral sliding surface function is designed, and the resulting sliding mode dynamics is a full-order Markovian jump singular stochastic system. By introducing some specified matrices, a new sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics. Then, a SMC law is synthesized for reaching motion. Moreover, when there exists an external disturbance, the ℒ 2 disturbance attenuation performance is analyzed for the sliding mode dynamics. Some related sufficient conditions are also established.