We study the bifurcation of limit cycles from the periodic orbits of a 4–dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first order expansion of the displacement function with respect to the small parameter. Moreover, this upper boun...

This paper studies the minimum switching control problem for a system of coupled double integrators with on-off input signals, in the presence of a constant disturbance term. This type of problem is relevant to a variety of applications in which the number of transitions of on-off actuators must be minimized, in order to prevent actuator wear. Two solutions are presented in terms of steady stat...

With a quantizer, limit cycles oscillations are inevitable if the controller has integral action independent of the controller tuning. Proof: At steady state the average uss = r/|G(0)| does not generally match uq. With oscillations between two quantization levels, uss = uq1 · f + uq2 · (1− f ) [f = fraction of time at a given quantizer level]. Sinusoidal oscillations Consider the following system: