Stability and stability margin for a two-dimensional system

Author

Zhou, Tong

Author_Institution

Dept. of Autom., Tsinghua Univ., Beijing

Volume

54

Issue

9

fYear

2006

Firstpage

3483

Lastpage

3488

Abstract

In this paper, a necessary and sufficient condition is derived for the stability of the Fornasini-Marchesini (FM) first model proposed for two-dimensional (2-D) dynamic system descriptions. A connection has been established between the stability of this model and the structured singular value (SSV) of a constant matrix, which is now widely known in control theories. Based on this connection, a novel sufficient condition is obtained for the stability of the FM first model that is more computationally convenient in filter design. Numerical simulations show that this sufficient condition is usually less conservative than that of . Moreover, the stability margin of the FM first model is also investigated. It is shown that a 2-D system remains stable under parametric variations if and only if the SSV of a constant matrix is smaller than one

Keywords

matrix algebra; stability; two-dimensional digital filters; Fornasini-Marchesini first model; constant matrix; stability margin; structured singular value; two-dimensional dynamic system; Control theory; Filtering theory; Filters; Matrix converters; Nonlinear dynamical systems; Numerical simulation; Stability; Sufficient conditions; Two dimensional displays; Vectors; Fornasini–Marchesini first model; stability; stability margin; structured singular value; two-dimensional system;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2006.879300

Filename

1677913