Robust invertibility of switched linear systems

In this paper, we address the effects of uncertainties in output measurements and initial conditions on invertibility of the switched systems - the problem concerned with the recovery of the input and the switching signal using the output and the initial state. By computing the reachable sets and maximal error in the propagation of state trajectories through the inverse system, we derive conditions under which it is possible to recover the exact switching signal over a certain time interval, provided the uncertainties are bounded in some sense. In addition, we discuss separately the case where each subsystem is minimum phase and it is possible to recover the exact switching signal globally in time. The input, though, is recoverable only up to a neighborhood of the original input.