The problem of robustness optimization with respect to the gap metric in the context of discrete-time Linear time-varying(LTV)systems is considered,which involves the computation of the maximum stability margin.Based on the inner-outer factorization of operators in nest algebras,a formula for the maximum stability margin is derived.Furthermore,the existence of an optimal controller is proved for uniformly asymptotically time-invariant LTV systems.

In this paper, we study the robust stability of an infinite-dimensional discrete-time linear time-varying (LTV) networked control system (NCS) with time-varying structured uncertainty. Such an NCS consists of a pair of uncertain plant and controller, as well as an uncertain bilateral communication channel in between. The uncertainties in the plant and controller are described by the multiplicative perturbation in coprime factors. The communication channel between the plant and controller is described as a cascade of two-port networks whose transmission matrices are subject to linear time-varying structured dynamic uncertainties, which are norm bounded. Necessary and sufficient conditions for robust stability of the NCS are established.