Representation of switched systems by perturbed control systems

This work provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems whose dynamics are given by differential equations, and whose inputs consist of the original controls together with disturbances that evolve in compact sets. Several applications dealing with properties of stability with respect to inputs and of detectability, and their characterizations in terms of Lyapunov functions, are derived as consequences of the representation theorem for such switched systems, and more generally, for systems with switching signals governed by digraphs.