Structural Controllability of Switched Linear Systems

TL;DR

This paper investigates the structural controllability of uncertain switched linear systems using graph theory, providing necessary and sufficient conditions based on interconnection relations and graphical representations.

Contribution

It introduces graph-theoretic characterizations for structural controllability of switched linear systems with uncertain parameters, extending traditional controllability concepts.

Findings

Graph-based necessary and sufficient conditions established

Two types of graphical representations proposed

Framework applicable to systems with unknown or zero parameters

Abstract

This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the traditional controllability concept for dynamical systems, and purely based on the interconnection relation between the state variables and inputs through non-zero elements in the state matrices. In order to illustrate such a relationship, two kinds of graphic representations of switched linear systems are proposed, based on which graph theory based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented. Finally, the paper concludes with discussions on the results and future work.