Harmonic Hamiltonian test for the H∞ performance in linear continuous-time periodic systems

Author

Zhou, Jun ; Hagiwara, Tomomich ; Araki, Mituhiko

Author_Institution

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

Volume

2

fYear

2003

fDate

9-12 Dec. 2003

Firstpage

1795

Abstract

Using spectra and Fourier analyses in finite-dimensional linear continuous-time periodic (FDLCP) systems, a Hamiltonian test is derived for the H_∞ performance. Furthermore, by staircase truncation and the 2-regularized determinant of Hubert-Schmidt operators, a finite-dimensional version of the test is also developed, which lays the foundation for claiming a modified bisection algorithm to estimate the H_∞ norm of the FDLCP system via finite-dimensional LTI continuous-time models. The finite-dimensional Hamiltonian test is necessary, and claimed only via Fourier analysis of system matrices without the transition matrix of the FDLCP system.

Keywords

Fourier analysis; H^∞ optimisation; continuous time systems; harmonic analysis; matrix algebra; multidimensional systems; periodic control; spectral analysis; Fourier analyses; H÷ performance; finite-dimensional linear continuous-time periodic systems; harmonic Hamiltonian test; linear continuous-time periodic systems; modified bisection algorithm; spectral analysis; staircase truncation; Eigenvalues and eigenfunctions; Frequency response; Harmonic analysis; Hilbert space; Performance analysis; Riccati equations; Steady-state; System performance; System testing; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7924-1

Type

conf

DOI

10.1109/CDC.2003.1272873

Filename

1272873