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

• 成果类型: Article
• 署名作者: Yuan, Shuai; Lv, Maolong; Baldi, Simone; Zhang, Lixian
• 署名单位: Harbin Institute of Technology; Delft University of Technology; Southeast University - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3003647
• 发表日期: 2021
• 页码: 2250-2256
• 关键词: Switches; Lyapunov methods; Linear systems; Numerical stability; Stability criteria; asymptotic stability; Dwell-time switching; stability analysis; switched adaptive control; switched linear systems

摘要

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.