Discerning controllers for switching linear systems: Existence and genericity

This paper presents recent developments in the study of non-autonomous switching linear systems. For such systems, we address the issue of how to systematically design linear controllers allowing the active process mode to be observable from closed-loop data. The results are stated formally by introducing the notion of discerning controllers. Both existence and genericity problems are discussed. It is finally shown how a given family of discerning controllers can be implemented as a single hybrid system which preserves the discerning capability of the original controllers. Examples are discussed to substantiate the analysis.