Control for discrete-time fuzzy Markov jump systems with mode-dependent antecedent parts

Abstract

This paper is concerned with the control problem for a class of discrete-time fuzzy Markov jump systems (MJSs). Unlike the common assumption in the existing literature, the antecedent parts of fuzzy rules are mode-dependent, i.e., the premise variables and/or their fuzzy partitions can be different in different modes. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the existence conditions of the desired mode-dependent state feedback controller are derived such that the closed-loop system is stochastically stable and achieves a guaranteed performance in the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. Two examples, including a practical example of robot arm, are used to demonstrate the applicability of the obtained theoretical results.