Identification/reduction to a balanced realization via the extended impulse response gramian

Author

Ang, E.-J. ; Sreeram, V. ; Liu, W.Q.

Author_Institution

Dept. of Electr. & Electron. Eng., Western Australia Univ., Nedlands, WA, Australia

Volume

40

Issue

12

fYear

1995

fDate

12/1/1995 12:00:00 AM

Firstpage

2153

Lastpage

2158

Abstract

A new identification/reduction algorithm for linear, discrete time-invariant (LDTI) systems is proposed which is based on the extended impulse response gramian first defined here for LDTI systems. The reduction algorithm employs singular value decomposition to retain states corresponding to dominant singular values of these gramians. The proven properties of the reduced order models include convergence to a balanced realization with conditional controllability, observability, and asymptotic stability. A suboptimal property of the model (in minimizing an impulse response error norm) is also demonstrated. The proposed technique can handle impulse response data of deterministic or stochastic nature for system identification application

Keywords

MIMO systems; asymptotic stability; controllability; discrete time systems; identification; linear systems; observability; reduced order systems; singular value decomposition; transient analysis; transient response; MIMO systems; asymptotic stability; controllability; convergence; impulse response gramian; linear discrete time-invariant systems; observability; reduced order models; reduction algorithm; singular value decomposition; system identification; Asymptotic stability; Continuous time systems; Controllability; Convergence; MIMO; Observability; Reduced order systems; Singular value decomposition; Stochastic systems; System identification;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.478344

Filename

478344