Robust stabilization of polytopic discrete-time systems with time-varying delay in the states

This paper presents less conservative LMIs conditions for robust stability analysis and for robust controller design of uncertain discrete-time systems with time-varying delay in the state vector. The uncertainty, supposed to be described in the polytopic framework, affects all matrices of the system. The proposed conditions are convex and delay dependent. The main idea is to apply a well-known parameter dependent Lyapunov-Krasovskii (L-K) function and, by using Finsler´s Lemma and Jensen´s Inequality, to decouple matrices of the system from the matrices of the L-K function. Extensions to deal with decentralized control, input delay and static output delay are included. It is shown by means of several numerical examples, including some motivated by real process, that this approach leads to less conservative results.