Homogeneous polynomial Lyapunov functions for piecewise affine systems

This paper addresses the construction of piece-wise homogeneous polynomial Lyapunov functions (PHPLFs) for piecewise affine (PWA) systems. Sufficient conditions for the existence of PHPLFs of a given degree for both continuous-time and discrete-time PWA systems are obtained in terms of linear matrix inequalities (LMIs). The result contains existing results based on piecewise quadratic Lyapunov functions as special cases and provides a less conservative assertion of the stability of PWA systems, which is supported by numerical examples.