Stability Analysis and Controller Design of the Nonlinear Switched Systems via T-S Discrete-Time Fuzzy Model

esses etc, can be appropriately described by the switched model [3-8]. In this paper, we proposed an innovative representation modeling of the Takagi-Sugeno (T-S) fuzzy switched discrete-time system. The simulation of stability analysis methods based on Lyapunov stability theorem to study the stability and switching law design for the T-S fuzzy switched discrete-time systems. Sufficient conditions for quadratic asymptotic stability are presented and stabilizing switching laws of state-dependent form are designed. Furthermore, these methods can be applied to cases when all individual systems are unstable. The parallel distributed compensation (PDC) is employed to design fuzzy controllers from the T-S fuzzy models. The stabilization analysis is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Finally, a numerical example and an illustrative example based on the chemical process example are given to show the merits of the proposed approach, respectively. Recently, some stability conditions and stabilization approaches have been proposed for the switched discrete-time systems. Ref. [9] studied stability property for the switched systems which are composed of a continuous-time LTI subsystem and a discrete-time LTI subsystem, when the two subsystems are Hurwitz and Schur stable, respectively, and have shown that if the subsystem matrices are symmetric, then a common Lyapunov function exists for the two subsystems and that the switched system is exponentially stable under arbitrary switching. Ref. [10, 11] studied robust stability analysis and control synthesis of uncertain switched systems. Ref. [12] has shown to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws. Ref. [13] studied the quadratic stabilization of discrete-time switched linear systems when a designed switching rule is imposed upon the feedback controller of subsystems, and studied quadratic stabilization of switched system with norm-bounded time-varying uncertainties. The event-driven scheduling strategy for constructing switching law to stabilize the switched system presented in [14]. There exists a switched quadratic Lyapunov function to check asymptotic stability of the switched discrete-time system in [15].