Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this paper, uncertain discrete-time systems with delayed states are investigated. The uncertainty is supposed to belong to a known convex polytope and can affect all system matrices. Sufficient linear matrix inequality conditions are given for the computation of H infinity-guaranteed costs and for the design of robust state feedback gains assuring an H infinity attenuation level. The conditions proposed here can assure robustness irrespective of the value of the delay and, differently from other approaches in the literature, are formulated as convex optimization problems. If the delay is known and the delayed states are available, a feedback gain depending on past values of the state can be used to improve the closed-loop performance of the system. As illustrated by numerical examples, including the model of an industrial electric heater, the proposed techniques are simple to be applied and can lead to less conservative results when compared with other conditions from the literature.263357373Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)