L norm simultaneous system approximation

Abstract

In this paper the L. nonn optimal simultaneous system approximation problem is studied. Various LMI based approaches to solve the simultaneous L. norm system approximation problem are developed. Computational schemes based on LMI based optimization techniques are derived. Examples are given to illustratethe results. KEYWORDS optimal (weighted) L_ (simultaneous) approximation; LMI basedconvex optimization INTRODUCTIONH_ norm and associated optimization problems in control, filtering and estimation have been proven to be very meaningful. A vast amount of literature on robust control and H _ optimal control has been developed since theearly 1980s. 1 It is often desirable to have a low order nominal plant since the degree of the controllers obtained by modem control design schemes such as LQG and H_ optimal control theory will be the same as the plant degree. The problem of model reduction has always attracted much attention and many model reduction schemes have been reported in the literature. The 11.11_ is widely accepted to be the most relevant measure for approximation error for robustness considerations.The L_ simultaneous model approximation problem is defined below. Definition JGiven G1(s), G 2(s), ... , GN(s) all in RL_ and weights Wi(s) E RH., find Gr(s) E RL_ with specified number of stable and unstable poles such that is minimized.