Abstract

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 bound is reached. For proving this result we use the averaging method in a form where the differentiability of the system is not needed.