Robust stabilization for a class of uncertain discrete-time switched linear systems

The problem of robust stabilization for a class of discrete-time switched linear systems with norm-bounded time-varying uncertainties is investigated. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable for all admissible uncertainties under the constructed switching rule. Based on the multiple Lyapunov functions approach and matrix inequality technique, a new condition for the existence of state feedback control law and switching rule is derived. The condition can be dealt with as linear matrix inequalities (LMIs) if some scalars parameters are selected in advance. An example illustrates the effectiveness of the proposed results.