This paper deals with uncertain discrete-time systems with time varying delay affecting the state vector. It is considered that the uncertainties are represented in a polytopic domain and they may be present in all matrices of the model of the system. Conditions expressed as Linear Matrix Inequalities (LMIs) are proposed for the H∞ guaranteed cost computation and for the design of robust state feedback control gains that minimize the H∞ norm from the perturbation input to the system output. These conditions are established by using parameter dependent Lyapunov-Krasovskii (L-K) functions. Slack matrix variables - via Finsler's Lemma - are employed to decouple the matrices of the system from the L-K function ones. The "Jensen's inequality" is used to handle crossed terms in the development of the conditions, yielding a less conservative over bound w.r.t. other approaches in the literature. The provided conditions are delay-dependent. Numerical examples are presented to illustrate the eficacy of the proposed conditions and they are used to establish comparisons with other techniques available in the literature.
Time-varying delay; discrete-time systems; H∞ robust control; linear matrix inequalities; parameter dependent Lyapunov-Krasovskii function; Finsler's Lemma; Jensen's inequality
