Model Approximation of Differential and Discrete LRPs

Abstract

This chapter studies the model approximation for both differential and discrete LRPs under a Hankel norm performance. The essence of the Hankel optimal model approximation problem is to find a desired lower-order model such that the Hankel norm of the difference between the original system and the desired lower-order one satisfies a prescribed Hankel norm bound constraint. For a given high-order differential (or discrete) LRP, our attention is focused on two cases: Case 1. the general case, the orders of both the process state and the pass profile are reduced simultaneously. Case 2. the special case, only the order of the process state is reduced and the pass profile is kept to its original order. In these connections, Hankel norm performances are first established for differential and discrete LRPs, respectively, and the corresponding model approximation problem is solved by utilizing the projection approach.