Construction of Polyhedral Lyapunov Functions for Discrete-Time Systems

In this paper we make use of the alternative converse Lyapunov theorem presented in [1] for specific classes of systems. We show that the developed converse Lyapunov theorem can be used to establish non–conservatism of a particular type of Lyapunov functions. Most notably, a proof that the existence of conewise linear Lyapunov functions are non– conservative for globally exponentially stable (GES) conewise linear systems is given and, as a by–product, tractable construction of polyhedral Lyapunov functions for linear systems is attained. keyword: Conewise linear systems, Polyhedral Lyapunov functions