A step-wise procedure for reduced order approximation in the ν-gap metric

Abstract

Recent results on reduced-order approximation in the ν-gap metric, characterised in terms of a non-convex feasibility problem, are investigated further. A detailed analysis of the properties of the constituent rank constrained Linear Matrix Inequalities, when the nominal system has an LQG-balanced state-space realisation, reveals that it is possible to construct a feasible point directly for a particular choice of reduced order and ν-gap error. This gives rise to a step-wise procedure, based on constructing an optimal approximant at each step. While as of yet, the freedom in the parameterisation of optimal approximants has not been exploited, the new stepwise technique developed in this pape..