Finite-Time Stabilization of Discrete-Time Switched Nonlinear Systems Without Stable Subsystems via Optimal Switching Signal Design

Abstract

This paper investigates the finite-time exponential stability analysis and stabilization problem of discrete-time switched nonlinear systems without stable subsystems. In the stability analysis, the Takagi–Sugeno (T–S) fuzzy model is employed to approximate nonlinear subsystems. With two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce switched fuzzy systems with approximation errors, which inherently contain both the features of the switched systems and T–S fuzzy systems. By constructing the “decreasing-jump” piecewise Lyapunov-like functions and minimum dwell time technique, a finite-time exponential stability of switched fuzzy systems with bounded approximation errors is obtained. Then, based on the finite-time exponential stability, a multiobjective evolution algorithm (nondominated sorting genetic algorithm, NSGA-II), which considers two conflicting objectives, such as the average convergence error and the average switching cost, is proposed to generate tradeoff switching sequences to stabilize the discrete-time switched nonlinear systems over a finite-time interval. A numerical example and a practical example are provided to illustrate the effectiveness of the stability and the algorithm, respectively.