Minimiza？？o do custo H∞ de sistemas incertos discretos no tempo com atraso nos estados

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.