Robust Stabilization of Switched Linear Systems, Based on State Feedback Observer and Dwell Time Switching Signal

Stabilization of switched linear systems is one of the most important problems in the area of switched systems. In this paper، a design method for robust stabilization of parametric uncertain switched linear systems is proposed in terms of linear matrix inequalities. First، a method is proposed assuming that all states are available. This method designs the state feedback gains، such that the closed-loop system to be robustly asymptotically stable under switching signals with the known minimum dwell time. Since the states are unmeasurable in some practical systems، the method is then extended to the practical cases، in which the outputs are just available. The observer-based stabilizing state feedback gains are designed to stabilize such systems robustly for dwell time switching signals. The asymptotic stability of the proposed methods is proved under the assumption that all the nominal subsystems are controllable and observable. Then، the method is also generalized for robust stabilization of uncertain switched linear systems under any arbitrary switching signal. The correctness and effectiveness of the results are illustrated by some numerical examples.