Frequency Weighted H∞ Model Reduction Based on LMI

This paper treats the problem of a frequency-weighted optimal H-infinity model reduction problem for linear time-invariant (LTI) systems. An algorithm based on the LMI is derived to solve the frequency weighted H-infinity model reduction problem. The aim of the algorithm is to minimize H-infinity norm of the frequency-weighted truncation error between a given LTI system and its lower order approximation. Necessary and sufficient conditions for solving this problem is to meet a series of rank constraints, which generally lead to a non-convex feasibility problem. In addition, it has ensured the stability of reduced-order model when both stable input and output weights are included. Compared with the existing algorithm, the error in this paper is relatively small. An efficient model reduction scheme based on cone complementarity algorithm (CCA) is proposed to solve the non-convex conditions involving rank constraint.