Title :
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
fDate :
2/1/2002 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
