Stability analysis of two-dimensional systems by means of finitely constructed bilateral quadratic forms

Author

Ooba, Tatsushi ; Funahashi, Yasuyuki

Author_Institution

Nagoya Inst. of Technol., Japan

Volume

49

Issue

11

fYear

2004

Firstpage

2068

Lastpage

2073

Abstract

Asymptotic stability of two-dimensional (2-D) systems in the state-space representation is studied. The concept of finitely constructed bilateral quadratic forms is introduced for the set of bilateral sequences of vectors, and the positivity of a bilateral quadratic form is characterized in terms of the solvability of an algebraic Riccati matrix inequality. A Lyapunov-like stability analysis of 2-D systems is conducted by resorting to positivity tests for a sequence of bilateral quadratic forms generated by a recurrence formula. The effectiveness is proved in an illustrative example.

Keywords

Riccati equations; asymptotic stability; linear matrix inequalities; multidimensional systems; state-space methods; algebraic Riccati matrix inequality; asymptotic stability; bilateral quadratic form; state-space representation; two-dimensional system; Automatic control; Control systems; Filtering; Linear systems; Noise robustness; Riccati equations; Robust control; Stability analysis; Stochastic resonance; Stochastic systems; 65; Algebraic Riccati matrix inequalities; positive bilateral quadratic forms; stability robustness analysis; state-space stability; two-dimensional systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2004.837532

Filename

1356132