Computation of the gap metric for asymptotically time-invariant linear time-varying systems

In this paper, we study the problem of computing the TV directed gap metric for asymptotically time-invariant linear time-varying systems. Based on duality theory, a computational approach to the TV directed gap metric is developed. We in this paper consider the algebras of discrete time, time-varying systems which are asymptotically time-invariant, in the sense that as time evolves the time-varying transfer operator uniformly (or strongly) converges to a time-invariant transfer operator on an appropriate Hilbert space of input-output signals.