Sliding Sector-Based Variable Structure Control of Continuous-Time Markov Jump Linear Systems Subject to Unknown Transition Rates

• Published in: Mathematical problems in engineering Vol. 2013; no. 2013; pp. 1 - 9
• Main Authors: Xue, Yanmei, Liu, Xiao-Mei, Yang, Jianwei
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2013; John Wiley & Sons, Inc
• Subjects: Boundaries; Continuity (mathematics); Control stability; Design; Design engineering; Engineering; Euclidean space; Linear matrix inequalities; Linear systems; Markov analysis; Markov processes; Mathematical analysis; Matrix methods; Robust control; Sliding; Stability; Theory; Variable structure control; China
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2013/364726

Based on sliding sector technique, the variable structure control for a class of uncertain continuous-time Markovian jump linear systems (MJLS) is investigated. The elements in the transition rate matrix include completely known, boundary known, and completely unknown ones. First, the related notions about sliding sector for continuous-time Markov jump linear systems are given; then based on linear matrix inequalities (LMIs) technique, sufficient conditions for the design of the sliding sector are provided. Second, a variable structure control law is presented to guarantee the mean-square quadratic stability of the closed-loop system in spite of the effects of the existing uncertainties and unknown/uncertain transition rates. Finally, an example is given to verify the validity of the theoretical results.