Stability analysis and H<inf>∞</inf> controller design of a class of switched discrete-time fuzzy systems

In this paper, the problems of stability analysis and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller design of a class of switched nonlinear systems are investigated. In a classical way, the modeling of the systems is approached by switched fuzzy systems, and both fast switching and slow switching are considered there. In particular, for slow switching scheme, a new mode-dependent average dwell time switching is proposed for the underlying switched fuzzy systems. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> state-feedback controller is derived. A numerical example is given to show the validity and potential of the theoretical results.