2-D BIBO stability using 1-D wave model

Author

Aravena, Jorge L.

Author_Institution

Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA

Volume

39

Issue

7

fYear

1992

fDate

7/1/1992 12:00:00 AM

Firstpage

570

Lastpage

576

Abstract

The bounded-input, bounded-output (BIBO) stability of 2-D shift-invariant systems is studied using the concept of the wave advance model, which converts the 2-D equation into a 1-D time-varying format. It is shown that the wavefront 1-D discrete Fourier transforms evolve according to a conventional time-invariant equation. The propagation model is used to develop 2-D BIBO stability criteria. The most general criterion is necessary and sufficient for BIBO stability of systems without singularities of the second kind on the unit bidisk. The criteria are sufficient when applied to 2-D systems with singularities of the second kind. In fact, this kind of singularity appears as a loss controllability (pole/zero cancellation) in a related 1-D observable canonical state equation. The approach proposed shows very clearly the effect of the numerator in the stability of such systems. The stability analysis of singularities can be carried out with conventional algebraic tools

Keywords

fast Fourier transforms; stability criteria; transfer functions; 1D discrete Fourier transforms; 1D time varying format; 1D wave model; 2D shift invariant systems; BIBO stability; loss controllability; observable canonical state equation; pole/zero cancellation; propagation model; second kind singularities; stability criteria; time-invariant equation; transfer function; wave advance model; Controllability; Discrete Fourier transforms; Equations; Frequency; History; Poles and zeros; Power system modeling; Stability analysis; Stability criteria; Sufficient conditions;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.257290

Filename

257290