Delay-Dependent Robust Stabilizability for Uncertain Discrete Time-Delay Systems

The problem of robust control for discrete time-delay systems with norm-bounded uncertainties was studied. A new sufficient condition of delay-dependent robust stabilizability was derived by introducing a zero formula and free weighting matrices. An explicit expression of the desired controller was also developed based on the solution of linear matrix inequalities (LMIs). Without any system transformation or inequalities to estimate the upper bound of the cross terms in the forward difference of Lyapunov functional, the corresponding conservatism on the stability condition is reduced. Numerical examples are given to illustrate the effectiveness of design procedure