On the use of gap metric for model selection in multilinear model-based control

One way to design the control of a nonlinear system is to use a set of linear models that are close to the nonlinear system. This gives rise to a need to define the concept of closeness. Since systems can be visualized as input-output operators, a natural distance concept would be the induced operator norm. Yet, the norm cannot be generalized as a distance measure. The aim of this paper is to discuss the application of a distance measure between systems, the gap metric, in order to select a reduced set of models that contain nonredundant process information for robust stabilization of feedback systems based on multimodel controller design.