H-infinity model reduction with guaranteed suboptimality bound

A family of new polynomial time algorithms is introduced for optimization of reduced order models of linear time-invariant (LTI) systems. It is proven that, as a suboptimal approach to the task of minimizing H-infinity norm of model reduction error, some of these algorithms have important advantages over the classical Hankel optimal model reduction technique: they produce better lower bounds for achievable H-infinity approximation error, and generate reduced models with a guaranteed a-priori relative error bound which depends on dimension of the reduced system only. The new approach has several advantages in practical large scale model reduction as well. It works with a black box oracle capable of measuring or estimating quality of reduced model candidates, and hence does not require full knowledge of a state space model of the system to be reduced. It can also be applied in the case when the system to be reduced is represented by a finite number of samples of its frequency or time domain response