On rigorous integration of continuous piecewise linear systems

Abstract

In this work, rigorous methods to compute solutions of continuous piecewise linear systems are presented. A general technique, based on integrating a perturbed linear system, is described to compute enclosures of trajectories crossing planes where the vector field in not smooth. Algorithms to compute enclosures of trajectories passing arbitrarily close to unstable equilibria are proposed. The usefulness of the methods is shown by proving the existence of trapping regions enclosing three different types of chaotic attractors existing in the Chua’s circuit.