Robust Stabilization of Linear Switched Systems with Unstable Subsystems

Martín-Antonio Rodríguez-Licea,Juan Prado Olivares,Francisco-J Perez-Pinal

doi:10.3390/app8122620

Abstract

This paper deals with the robust stability of a class of uncertain switched systems with possibly unstable linear subsystems. In particular, conditions for global uniform exponential stability are presented. In addition, a procedure to design a mode dependent average dwell time switching signal that stabilizes a switched linear system composed of diagonalizable subsystems is established, even if all of them are stable/unstable and time-varying (within design bounds). An illustrative example of the stabilizing switching law design and numerical results are presented.

Highlights

In recent years, the interest in Switched Linear Systems (SLS) has increased because of its capability to represent complex nonlinear systems in a more tractable math form, and their analysis has spread out as a new branch of stability and control especially for SLS with one or more unstable subsystems, while some of the Lyapunov and other theories can be applied to those with all stable subsystems [1,2].State-dependent and time-dependent switching signals are the main approaches to design stabilizing switching laws
This work was focused on four main areas: adaptive tracking using extended and average dwell times, adaptive asymptotic tracking, robust adaptive tracking, adaptive stabilization with time-varying delays, and robust stability and stabilization with switching delays
It can be noticed from the above state of the art that the robust stability and stabilizing switching Mode-Dependent Average Dwell Time (MDADT) signal design for SLS with any combination of stable/unstable systems is a topic of recent interest for researchers and industry

Summary

Introduction

The interest in Switched Linear Systems (SLS) has increased because of its capability to represent complex nonlinear systems in a more tractable math form, and their analysis has spread out as a new branch of stability and control especially for SLS with one or more unstable subsystems, while some of the Lyapunov and other theories can be applied to those with all stable subsystems [1,2]. This work was focused on four main areas: adaptive tracking using extended and average dwell times, adaptive asymptotic tracking, robust adaptive tracking, adaptive stabilization with time-varying delays, and robust stability and stabilization with switching delays It can be noticed from the above state of the art that the robust stability and stabilizing switching MDADT signal design for SLS with any combination of stable/unstable systems is a topic of recent interest for researchers and industry. In this paper, the robust stability for diagonalizable uncertain SLS is analyzed, and a new result is presented Such analysis allows the design of a stabilizing switching MDADT signal, and it is not restricted to positive systems, nor to all stable/unstable subsystems.

Preliminaries

Simulations

Conclusions