Discussion on Controllability of Switched Linear System with Constant Input Matrix

Abstract:

This paper re-examines the controllability of a class of switched linear systems which has different systematic matrices and the same input matrix. Investigations reveal that the necessary and sufficient condition derived in literatures is a false proposition: it only holds for second-order systems, while the necessity is not always true for systems of third and higher order. We also prove that the first invariant subspace is a proper subset of controllable state set rather than the whole of it. Finally, a counterexample is presented to illustrate the conclusion.