Bifurcation of limit cycles from a four-dimensional center in control systems

We study the bifurcation of limit cycles from the periodic orbits of a four-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.