A Hankel matrix approach to singular system realization theory

Author

Gray, W. Steven ; Verriest, Erik I. ; Lewis, Frank L.

Author_Institution

Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA, USA

fYear

1990

fDate

5-7 Dec 1990

Firstpage

73

Abstract

A Hankel matrix approach to singular system realization theory is presented. The focus is exclusively on discrete-time or descriptor systems. Based on definitions of reachability and observability, the notion of a system Hankel matrix is first defined. The system Hankel matrix is then shown to have reachability-observability matrix factorizations which can be used to solve the realization synthesis problem. The notion of a balanced realization for singular systems is derived using the singular value decomposition of the system Hankel matrix. The theory is applied to synthesizing realizations which have minimum parametric sensitivity properties. It is demonstrated that such realizations are related to the notion of balancing

Keywords

control system synthesis; discrete time systems; matrix algebra; observability; Hankel matrix; balanced realization; descriptor systems; matrix factorizations; minimum parametric sensitivity; observability; reachability; realization synthesis; singular system realization theory; Difference equations; H infinity control; Linear systems; Matrix decomposition; Observability; Physics computing; Singular value decomposition; Space technology; State-space methods; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1990., Proceedings of the 29th IEEE Conference on

Conference_Location

Honolulu, HI

Type

conf

DOI

10.1109/CDC.1990.203549

Filename

203549