A note on optimal control of autonomous switched systems on a finite time interval

This paper deals with the problem of optimal control of continuous-time autonomous linear switched systems on a finite control horizon. Sufficient conditions for optimality are developed using Hamilton-Jacobi-Bellman theory. The optimal switching signal is computed through backward integration of a differential Lyapunov equation coupled with the dynamic of the switched system. The switching signal is proved to be independent from a scaling of the initial state, and a numerical procedure based on the discretization of the state space is proposed to compute the optimal switching