This paper introduces the concept of consistency for continuous-time switched linear systems having the switching function as a primary control signal to be designed. A switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems. Conditions under which amin-type switching strategy is strictly consistent for the classes of H-2 and H-infinity performance indexes are determined. This property makes clear the importance of switching systems control design in both theoretical and practical application frameworks. Moreover, with this property it is not necessary to assume that all the subsystems are not stable in order to make a switching strategy design problem well posed. The theory is illustrated by means of several academic examples.