Lyapunov-Equation-Based Stability Analysis for Switched Linear Systems and Its Application to Switched Adaptive Control
S. Yuan (Harbin Institute of Technology, TU Delft - Team Bart De Schutter)
Maolong LV (TU Delft - Team Bart De Schutter)
S. Baldi (Southeast University, TU Delft - Team Bart De Schutter)
Lixian Zhang (Harbin Institute of Technology)
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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.