Bounds on the number of switchings with scale-independent hysteresis: applications to supervisory control

In this paper we analyze the scale-independent hysteresis switching logic introduced in recent work. We show that, under suitable "open-loop" assumptions, one can establish an upper bound on the number of switchings produced by the logic on any given interval. This bound comes as a function of the variation of the inputs to the logic on that interval. In this paper it is also shown that, in a supervisory control context, this leads to switching that is slow-on-the-average, allowing us to study the stability of hysteresis-based adaptive control systems in the presence of measurement noise.