Bifurcation of limit cycles from a two-dimensional center inside RnRn

We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in RnRn perturbed inside a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that at most one limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.