Stability analysis of planar continuous piecewise linear systems

Abstract

In this paper, planar continuous piecewise linear (PCPWL) systems composed of more than two linear subsystems are investigated. Instead of using Lyapunov method, we study the behavior of the PCPWL system directly to give the stability analysis. When there exist eigenvectors for the PCPWL system, the subsystem stability ensures the global stability. If there are no eigenvectors, the one-circle-gain determines the global stability. Besides, we claim that PCPWL system with three stable subsystems is always globally stable if each subsystem has distinct real eigenvalues. Simulation results illustrate the proposed stability tests.