Time-domain v-gap robustness analysis for shift-invariant systems

Abstract

A $\nu$-gap measure of distance between linear time-invariant systems is defined in terms of projections onto system graphs directly, without appealing to the existence of normalised strong graph representations as in the literature. A robust stability result is derived by exploiting an assumption on the compactness of a Hankel-type operator in a similar manner to recent developments on time-varying generalisation of the $\nu$-gap metric. For a class of distributed-parameter systems, the proposed $\nu$-gap reduces to the original frequency-domain definition.