Exact Stability Analysis of 2-D Systems Using LMIs

Author

Ebihara, Yoshio ; Ito, Yoshimichi ; Hagiwara, Tomomichi

Author_Institution

Dept. of Electr. Eng., Kyoto Univ.

Volume

51

Issue

9

fYear

2006

Firstpage

1509

Lastpage

1513

Abstract

In this note, we propose necessary and sufficient conditions for the asymptotic stability analysis of two-dimensional (2-D) systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions that enable us to analyze the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that, by employing the generalized S-procedure, we can derive smaller size of LMIs so that the computational burden can be reduced

Keywords

asymptotic stability; control system analysis; linear matrix inequalities; multidimensional systems; 2D systems; LMI; Schur stable complex matrices; asymptotic stability analysis; linear matrix inequalities; nonsingularity analysis; parameter dependent complex matrices; Asymptotic stability; Eigenvalues and eigenfunctions; Error correction; Error correction codes; Linear matrix inequalities; Matrices; Notice of Violation; Riccati equations; Stability analysis; Two dimensional displays; Linear matrix inequalities (LMIs); stability analysis; two-dimensional (2-D) systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2006.880789

Filename

1695992