Lyapunov-Equation-Based Stability Analysis for Switched Linear Systems and Its Application to Switched Adaptive Control

Journal article (2021)

Authors

S. Yuan , Harbin Institute of Technology
S. Baldi Southeast University,
Lixian Zhang Harbin Institute of Technology
Copyright: © 2021 S. Yuan, Maolong Lv, S. Baldi, Lixian Zhang
DOI: https://doi.org/10.1109/TAC.2020.3003647
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Published Date

2021

Language

English

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Abstract

This article investigates the stability of continuous-time switched linear systems with dwell-time constraints. A fresh insight into this established problem is provided via novel stability conditions that require the solution to a family of differential Lyapunov equations and algebraic Lyapunov equations. The proposed analysis, which leads to a peculiar Lyapunov function that is decreasing in between and at switching instants, enjoys the following properties: it achieves the same dwell time as the well-known result in the research 'stability and stabilization of continuous time switched linear systems' by Geromel and Colaneri; it removes the increasing computational complexity of the linear interpolation method; it leads to a straightforward counterpart for discrete-time switched linear systems.We show the application of this methodology to the problem of adaptive control of switched linear systems with parametric uncertainties.

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