On model reduction in the ν-gap metric

The problem of reduced order approximation to within a specified ν-gap distance from a nominal model is considered. A condition for the existence of such an approximation is given in terms of two Lyapunov inequalities and a coupling rank constraint. When this condition is satisfied, a corresponding reduced order model can be constructed explicitly. From the perspective of behaviour in closed-loop, approximation in the ν-gap metric is appealing, since the ν-gap between two open-loop systems is a measure of the maximum possible difference in closed-loop behaviour with a given compensator