Relaxed stability and stabilization conditions for a class of switched fuzzy discrete systems

This paper introduces a innovated representation model, namely, a discrete-time switched fuzzy (DTSF) system, which differs from existing ones. In this model, a system is a switched system whose subsystems are all discrete-time Takagi-Sugeno (T-S) fuzzy systems. This class of systems can often more precisely describe continuous dynamics and discrete dynamics as well as their interactions in complex real-world systems, and then the systems can be designed switching law intelligently, which is to choose the subsystem whose behavior is the best according to some performance criterion. Then in this paper, the state feedback controllers for the proposed DTSF systems are built to ensure that the relevant closed-loop system is quadratically stable using switching technique and the multiple Lyapunov functions method. Finally, switching laws of the state-dependent form achieving system quadratic stability of the switched fuzzy system are given. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.