Stability of interconnected switched systems and supervisory control of time-varying plants

We discuss stability of a loop consisting of two asynchronous switched systems, in which the first switched system influences the input and the switching signal of the second switched system and the second switched system affects the first switched system's jump map. We show that when the first switched system has a small dwell-time and is switching slowly in the spirit of average dwell-time switching, all the states of the closed loop are bounded. We show how this result relates to supervisory adaptive control of time-varying plants. When the uncertain plant takes the form of a switched system with an unknown switching signal, we show that all the states of the closed-loop control system are guaranteed to be bounded provided that the plant's switching signal varies slowly enough.