Further Results on “Infinity Norms as Lyapunov Functions for Linear Systems”

This note continues on the results proposed in two previous papers for computing vector 1- or infin-norm based Lyapunov functions for linear discrete-time systems by presenting a finitely terminating algorithm for the construction of Lyapunov functions of that class. The algorithm utilizes the solution of a finite sequence of feasibility linear programs (LPs) with very few constraints or, equivalently, very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved