Reduced order models, or model reduction, have been used in many technologically advanced areas to ensure the associated complicated mathematical models remain computable. For instance, reduced order models are used to simulate weather forecast models and in the design of very large scale integrated circuits and networked dynamical systems.

For linear systems, the model reduction problem has been addressed from several perspectives and a comprehensive theory exists. Although many results and efforts have been made, at present there is no complete theory of model reduction for...