Hits:

Indexed by:期刊论文

Date of Publication:2016-10-02

Journal:INTERNATIONAL JOURNAL OF CONTROL

Included Journals:SCIE、EI、Scopus

Volume:89

Issue:10

Page Number:2083-2095

ISSN No.:0020-7179

Key Words:H-2-norm; linear time-varying periodic system; periodic Lyapunov differential equation; extended precise integration method; Fourier series expansion

Abstract:A new reliable algorithm for computing the H-2-norm of linear time-varying periodic (LTP) systems via the periodic Lyapunov differential equation (PLDE) is proposed. By taking full advantage of the periodicity, the transition matrix of the underlying LTP system associated with the PLDE is effectively computed by developing a novel extended precise integration method based on Fourier series expansion, where the time-consuming work for the computation of the matrix exponential and its related integrals in every sub-interval is avoided. Then, a highly accurate and efficient algorithm for the PLDE is derived using the block form of the transition matrix. Thus, the H-2-norm is evaluated by solving a simple first-order ordinary differential equation. Finally, two numerical examples are presented and compared with other algorithms to verify the numerical accuracy and efficiency of the proposed algorithm.