Exponential Stability of Continuous-Time Piecewise Affine Systems

Leonardo Cabral, Giorgio Valmorbida, João Manoel Gomes da Silva

Abstract: This letter addresses the problem of global exponential stability analysis of the origin of continuous-time Continuous Piecewise Affine (CPWA) systems. The stability analysis in this letter considers Piecewise Quadratic (PWQ) Lyapunov Functions (LF) and a ramp-based implicit representation of PWA systems. Sufficient convex stability conditions are obtained in the form of a Semidefinite Programming (SDP) problem. Two major benefits arise from the proposed results: i) the need for equality constraints to ensure the continuity of the LF across the boundaries of the sets of the partition is withdrawn; ii) there is no need to consider separate SDP conditions for each set of the partition, which simplifies the application of the conditions. The effectiveness of the proposed method is illustrated in numerical examples.