On the limit cycles of a class of discontinuous piecewise linear differential systems

In this paper we consider discontinuous piecewise linear differential systems whose discontinuity set is a straight line L which does not pass through the origin. These systems are formed by two linear differential systems of the form x = Ax ± b. We study the limit cycles of this class of discontinuous piecewise linear differential systems. We do this study by analyzing the fixed points of the return map of the system defined on the straight line L. This kind of differential systems appear in control theory.