Lyapunov stability of two-dimensional digital filters with overflow nonlinearities

Author

Liu, Derong

Author_Institution

Dept. of Electr. & Comput. Eng., Stevens Inst. of Technol., Hoboken, NJ, USA

Volume

45

Issue

5

fYear

1998

fDate

5/1/1998 12:00:00 AM

Firstpage

574

Lastpage

577

Abstract

In this paper, the second method of Lyapunov is utilized to establish sufficient conditions for the global asymptotic stability of the trivial solution of zero-input two-dimensional (2-D) Fornasini-Marchesini state-space digital filters which are endowed with a general class of overflow nonlinearities. Results for the global asymptotic stability of the null solution of the 2-D Fornasini-Marchesini second model with overflow nonlinearities are established. Several classes of Lyapunov functions are used in establishing the present results, including vector norms and the quadratic form. When the quadratic form Lyapunov functions are considered, the present results involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for 2-D digital filters with overflow nonlinearities

Keywords

Lyapunov methods; asymptotic stability; filtering theory; matrix algebra; state-space methods; two-dimensional digital filters; 2D Fornasini-Marchesini filters; Lyapunov stability; global asymptotic stability; null solution; overflow nonlinearities; positive definite matrices; quadratic form; two-dimensional digital filters; vector norms; zero-input 2D state-space digital filters; Cellular networks; Cellular neural networks; Circuits; Digital filters; Lyapunov method; Neural networks; Nonlinear control systems; Region 4; Region 5; Region 8;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.668870

Filename

668870