Stability analysis of continuous-time periodic systems via the harmonic analysis

Author

Zhou, Jun ; Hagiwara, Tomomichi ; Araki, Mituhiko

Author_Institution

Dept. of Electr. Eng., Kyoto Univ., Japan

Volume

47

Issue

2

fYear

2002

fDate

2/1/2002 12:00:00 AM

Firstpage

292

Lastpage

298

Abstract

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDLCP model whose transition matrix can be determined explicitly. By extending the Gerschgorin theorem to linear operators on the linear space l₂, yet another disc-group criterion is derived, which is only sufficient. Stability of the lossy Mathieu equation is analyzed as a numerical example to illustrate the results

Keywords

Lyapunov methods; asymptotic stability; continuous time systems; harmonic analysis; linear systems; multidimensional systems; periodic control; stability criteria; time-varying systems; Gerschgorin theorem; disc-group criterion; finite-dimensional linear continuous-time periodic systems; generalized Lyapunov equation; harmonic Lyapunov equation; harmonic analysis; linear operators; linear space; lossy Mathieu equation; necessary and sufficient stability criterion; stability analysis; stability test; transition matrix; Automatic control; Costs; Equations; Harmonic analysis; Logistics; Lot sizing; Optimal control; Production control; Stability analysis; Stability criteria;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.983361

Filename

983361