On Extended Model Order Reduction for Linear Time Delay Systems

This chapter presents a so-called extended model-reduction technique for linear delay differential equations. The presented technique preserves the infinite-dimensional nature of the system and facilitates the preservation of properties such as system parameterizations (uncertainties). It is proved in this chapter that the extended model-reduction technique also preserves stability properties and provides a guaranteed a-priori bound on the reduction error. The reduction technique relies on the solution of matrix inequalities that characterize controllability and observability properties for time delay systems. This work presents conditions on the feasibility of these inequalities, and studies the applicability of the extended model reduction to a spatio-temporal model of neuronal activity, known as delay neural fields. Lastly, it discusses the relevance of this technique in the scope of model reduction of uncertain time delay systems, which is supported by a numerical example.