Sliding mode control of MIMO Markovian jump systems. (June 2016)

• Record Type: Journal Article
• Authors: Zhu, Jiaming; Yu, Xinghuo; Zhang, Tianping; Cao, Zhiqiang; Yang, Yuequan; Yi, Yang
• Is Part Of: Automatica. Volume 68(2016)
• Page Start: 286
• Page End: 293
• Publication Date: 2016-06
• Subjects: Sliding mode control -- Markovian jump system -- Linear matrix inequality (LMI) -- Conditional probability -- Asymptotical stability; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.01.070
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper addresses the sliding mode control problem for uncertain MIMO linear Markovian jump systems. Firstly, by using the linear matrix inequality approach, sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the system on the sliding surfaces. Secondly, an equivalent control based sliding mode control is proposed, such that the closed-loop system can be driven onto the desired sliding surfaces in a finite time. Finally, combining with multi-step state transition probability, the reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. Simulation results are presented to illustrate the effectiveness of the proposed design method.