Abstract: One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions)problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of solutions of Carathéodory in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Furthermore, it is clear that when carrier signal h(t)=0, closed loop PWM DC-DC converters are not well-posed and when some condition is satisfied, closed loop PWM DC一DC converters with P controller are well-posed.