Anisotropy-based bounded real lemma for discrete-time systems with multiplicative noise

Abstract

A model of a discrete-time system with multiplicative noise is considered. For this model, a condition is derived under which the anisotropic norm of the system is bounded by the anisotropic norm of an auxiliary linear discrete-time stationary system with parametric uncertainty. Conditions for the anisotropic norm of the system with multiplicative noise to be bounded by a given positive number are obtained in terms of solutions of linear matrix inequalities and a single equation.