Regional Stability Analysis of Discrete-Time Piecewise Affine Systems

Leonardo Cabral, Giorgio Valmorbida, João Manoel Gomes da Silva

Abstract: In this article, we study the regional stability of discrete-time piecewise affine (PWA) systems. The proposed method for the stability analysis uses an implicit representation of PWA systems based on ramp functions, and it builds upon Linear Matrix Inequalities to verify the nonnegativity of piecewise quadratic (PWQ) functions in a given set. Verifying the nonnegativity of PWQ functions allows us to solve Lyapunov inequalities yielding a PWQ Lyapunov function of which a level set gives an estimate of the region of attraction of the origin. Numerical results illustrate the effectiveness of the proposed method.