Existence of non-symmetrical Lyapunov functions for linear systems

Abstract

Three non-symmetrical positive-definite functions that generate non-symmetrical domains of Rn are proposed as candidate Lyapunov functions for discrete-time free linear systems. Three sufficient conditions are given in R2n for these functions to become Lyapunov functions. The generated non-symmetrical domains are the stability domains for the class of dynamical discrete-time free linear systems that satisfy such conditions.