Criterion of Chaos for Switched Linear Systems with Controllers

In this paper, a sufficient criterion for time-invariant switched linear systems with controllers to be chaotic in the sense of Li–Yorke and Devaney is presented. The switched linear systems consist of an unstable subsystem with expanding flows and a controllable subsystem. It is exposed that the controllability of dynamic systems, instead of asymptotic stability, plays an important role in generating chaos. Finally, we give a numerical simulation for an example with some variable parameters to illustrate the validity of the result.