Robust control for discrete-time switched systems with constructing switching rule

The problem of robust control for a class of discrete-time switched systems with norm-bounded time-varying uncertainties is investigated. The purpose is to design a state feedback control law with constructing switching rule, such that, the closed-loop system is asymptotically stable for all admissible uncertainties under the constructed switching rule. By the introduction of additional matrices, 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.