A stable state-space realization in the formulation of H^∞norm computation

Author

Chang, B.-C.

Author_Institution

Bradley University, Peoria, IL, USA

Volume

Issue

fYear

1987

fDate

9/1/1987 12:00:00 AM

Firstpage

811

Lastpage

815

Abstract

In the two block H^inftyoptimization problem, usually we are given the state-space realizations of the proper rational matrices $R_{1}(s)$ and $R_{2}(s)$ whose poles are all the open right-half plane. Two problems are studied in the note. The first is the evaluation of $\\phi(s)R_{1}(s)$ at $s = s_{k}, k = 1, 2, ..., n$ , where $\\phi(s)$ is an inner function whose zeros ${s_{k}, k = 1, 2, ..., n }$ are the poles of $R_{1}(s)$ . This evaluation is essential if Chang and Pearson\´s method is used for computing the optimal H^inftynorm. The problem is solved in state space via the solutions of Lyapunov equations. Neither polynomial matrix manipulations nor numerical pole-zero cancellations are involved in the evaluation. The second problem is to find a stable state-space realization of $S(s) = U(s)R_{2}(s)$ where $U(s)$ is an inner matrix. This problem arises in the spectral factorization of $\\gamma ^{2} - R_{2}^{\\ast }R_{2}$ . Doyle and Chu had a method for constructing stable $S(s)$ based on a minimal realization of $R_{2}(s)$ . An alternate method is proposed. The alternate method does not require a minimal realization of $R_{2}(s)$ and only a Lyapunov equation is involved.

Keywords

H∞ optimization; Lyapunov methods, linear systems; Attenuation; Equations; Image analysis; Linear approximation; Optimal control; Polynomials; State-space methods; Weight control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1987.1104707

Filename

1104707

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=856613

A stable state-space realization in the formulation of H∞norm computation

Chang, B.-C.

jour

A stable state-space realization in the formulation of H^∞norm computation