Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This paper analyzes the concept of consistency for discrete-time switched linear systems having the switching function as a primary control signal to be designed, and also proposes a certification of how consistent is such switching function. A state feedback switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems. Under certain conditions, it is shown that a min-type switching strategy is strictly consistent for classes of H-2 and H-infinity performance indexes. This property makes clear the importance of switching systems control design in both theoretical and practical application frameworks. The theory is illustrated by means of academic examples. (C) 2013 European Control Association. Published by Elsevier Ltd. All rights reserved.193214219Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)