Stability Analysis, H_∞Control And Reachable Set Estimation Of Discrete-time Switched Systems

Switched systems are hybrid systems which consist of a collection ofsubsystems and a switching signal governing the switching among them. Due tothe system modeling capabilities, the switched system theory is widely used inthe mechanical industry, chemical industry, aviation industry and powerelectronics industry. As we can see, the most of studies are focused on switchedlinear systems with vast systematical results obtained. However, owing to itscomplexity, the investigation of switched nonlinear systems is relativelysomewhat limited. Moreover, for the switching signal, the studies of mode-dependent average dwell time switching are rarely mentioned. In addition, as animportant research direction in control theory, reachable set estimation ofswitched systems under bounded disturbances has almost not been investigatedso far. Based on the previous results, this paper is concerned with the problem ofstability analysis, H_∞control and reachable set estimation of discrete-timeswitched systems.Firstly, chapter2gives a brief introduction to multiply Lyapunov function.By the use of these tools, the stability condition of discrete-time switched linearsystem is given. For the nonlinear case, the switched nonlinear system ismodeled by switched fuzzy approach. The stability conditions under arbitraryswitching, average dwell time and mode-dependent average dwell time arederived for the switched fuzzy systems in this paper.Based on the stability results, the problem of H_∞controller design is alsostudied. In this paper, the l2-gain conditions for switched systems under mode-dependent average dwell time switching are first derived. Due to the “jumps” ofadjacent Lyapunov functions at switching instant, we can only get a weighted l2-gain. Furthermore, the H_∞controller design conditions for discrete-time switchedlinear systems under mode-dependent average dwell time switching and discrete-time switched fuzzy systems under arbitrary switching, average dwell time andmode-dependent average dwell time switching are obtained.Finally, chapter4investigates the problems of reachable set estimation ofdiscrete-time switched linear systems and discrete-time switched fuzzy systems under bounded disturbances. The basic method of reachable set estimation isproposed in this paper, and the reachable set estimation problem is converted intoan eigenvalue optimization problem. Based on this, a controller design method inorder to get a smallest reachable set is obtained.