Computation and stability analysis of limit cycles in piecewise linear hybrid systems
Résumé
Hybrid systems often exhibit periodic behaviours. Therefore, the computation and the stability analysis of hybrid limit cycles is an important problem. Recently, several techniques have been proposed for the stability analysis of periodic solutions. However, all of these assume that the cycle has previously been computed, which is not the easiest part of the work. In this paper, we present a method for the numerical computation of limit cycles in piecewise linear hybrid systems. It uses the concept of hybrid Poincare map and is an extension of the algorithms existing for smooth dynamical systems. An example is treated in order to show the results that can be obtained in practice.