Suboptimal switching control consistency analysis for discrete-time switched linear systems

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 H2H2 and H∞H∞ 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.