Robust stabilization of uncertain linear systems with input delay

This paper is concerned with robust stability and robust stabilization problems of uncertain linear systems with delayed state and delayed input respectively. The admissible uncertainty of the systems considered in this paper appears in quadratic constrained forms which take the well-known norm-bounded time-varying uncertainty as a special case. Delay-dependent results for the two addressed problems are derived using Razumikhin stability theorem and further algorithms are proposed which enable us to find suboptimal upper bounds for both cases and the controller gain matrix for the stabilization case using linear matrix inequalities (LMIs) technique.