An algorithm for model reduction of 2-D discrete time systems

Author

Premaratne, Kamal ; Jury, E.I. ; Mansour, M.

Author_Institution

Dept. of Electr. & Comput. Eng., Miami Univ., Coral Gables, FL, USA

Volume

37

Issue

9

fYear

1990

fDate

9/1/1990 12:00:00 AM

Firstpage

1116

Lastpage

1132

Abstract

In the context of model reduction of 2-D discrete time systems, several important properties of 2-D Gramians and balanced realizations are presented. Through a counterexample, the conjecture that the reduced model preserves stability is proven invalid. For separable systems, several interesting results regarding Gramians, norms, stability, and minimality are presented. For nonseparable systems, a simple, more efficient technique to compute Gramians is provided. The computation of Gramians in the separable case is possible through the solution of two pairs of discrete Lyapunov equations. An example is given to illustrate and justify the notions presented

Keywords

Lyapunov methods; discrete time systems; multidimensional systems; stability; 2-D Gramians; 2-D discrete time systems; balanced realizations; discrete Lyapunov equations; minimality; model reduction; norms; stability; Computational efficiency; Digital filters; Discrete time systems; Equations; Magnetic separation; Microcomputers; Reduced order systems; Roundoff errors; Stability; State-space methods;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.57600

Filename

57600