Robust H-infinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of H-infinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varyi ng norm-bounded parameter uncertainty and time delay in the state. First, t he problem of robust stability of the underlying system is investigated. Ne xt, we address the problem of robust H-infinity state feedback control in w hich both robust stability and a prescribed H-infinity performance are requ ired to be achieved irrespective of the uncertainty and time delay. It is s hown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.