Robust exponential stabilization of switched linear systems

The class of switched linear systems with norm-bounded uncertainties is considered here. Robust exponential stability and robust exponential stabilization problems are in focus. First, based on multiple Lyapunov function technique and Metzler matrices, sufficient conditions are derived such that the uncertain switched system is robustly exponentially stable for all uncertainties. Next, a design procedure is proposed for simultaneous construction of a switching rule (that employs only output information) and an associated state or output feedback controller that stabilize the closed loop system for all admissible uncertainties. All the proposed conditions are expressed in terms of bilinear matrix inequalities (BMIs) that can successfully solved as linear matrix inequalities (LMI) provided that some parameters are fixed in advance. Numerical examples are given to show the effectiveness of the proposed methods.