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

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 funct...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 25; no. 1; pp. 172 - 180
Main Authors: Mao, Yanbing, Zhang, Hongbin, Zhang, Ziang
Format: Journal Article
Language:English
Published: IEEE 01.02.2017
Subjects:
Control theory
Convergence
Exponential stability
minimum dwell time
Nonlinear systems
NSGA-II
Stability analysis
switched nonlinear systems
Switched systems
Switches
Takagi–Sugeno (T–S) fuzzy model
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary: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.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2016.2554139