A parametrization of piecewise linear Lyapunov functions via linear programming

In this paper, we present a parametrization of piecewise linear (PWL) Lyapu nov functions. To this end, we consider the class of all continuous PWL fun ctions defined over a simplicial partition. We take advantage of a recently developed high level canonical PWL (HL CPWL) representation, which express es the PWL function in a compact and closed form. Once the parametrization problem is properly stated, we focus on its application to the stability an alysis of dynamic systems. We consider uncertain non-linear systems and ext end the sector condition obtained by Ohta ct al. In addition, we propose a method of selecting an optimal candidate. One of the main advantages of thi s approach is that the parametrization and choice of the Lyapunov candidate , as well as the stability analysis, result in linear programming problems.