Sufficient conditions for strong structural controllability of uncertain linear time-varying systems

Abstract

In this paper, we extend the notion of strong structural controllability of linear time-invariant systems, a property that requires the controllability of each system in a specific class given by the zero-nonzero pattern of the system matrices, to the linear time-varying case ẋ (t) = A(t) · x(t) + B(t) · u(t), where A and B are matrices of analytic functions. It is demonstrated that the requirements for strong structural controllability of linear time-invariant systems are not sufficient for strong structural controllability of linear time-varying systems. Moreover, in the main result of this paper, sufficient conditions for strong structural controllability of linear time-varying systems are given and an algorithm for verifying this property is provided. Since time-invariant systems are included in the class of time-varying system, these conditions are also new sufficient conditions for strong structural controllability of time-invariant systems. Finally, the results are illustrated by means of an example.