A Separated Approach to Control of Markov Jump Nonlinear Systems With General Transition Probabilities

This paper is devoted to the control of Markov jump nonlinear systems with general transition probabilities (TPs) allowed to be known, uncertain, and unknown. With the help of the S-procedure to dispose the system nonlinearities and the TP property to eliminate the coupling between unknown TP and Lyapunov variable, an extended bounded real lemma for the considered system to be stochastically stable with the prescribed H_∞ performance is established in the framework of linear matrix inequalities. To handle the nonlinearity incurred by uncertain TP for controller synthesis, a separated method is proposed to decouple the interconnection between Lyapunov variables and controller gains. A numerical example is given to show the effectiveness of the proposed method.

I. Introduction

Over the past decades, much attention has been attracted to the field of Markov jump systems (MJSs). The reason is that this kind of system is suitable to model dynamic systems subject to random abrupt variations in their structures, and has widespread applications in target tracking, manufactory processes, and fault-tolerant systems [20], [37]. Up to date, many control issues have been intensively addressed for MJSs, such as control, sliding mode control, passive control, sampled-data control, and guaranteed cost control [5], [6], [13], [14], [17], [23]–[25], [31]–[36], [38].