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Indexed by:期刊论文

Date of Publication:2011-04-15

Journal:JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Included Journals:SCIE、EI

Volume:235

Issue:12

Page Number:3571-3588

ISSN No.:0377-0427

Key Words:Matrix recursive algorithm; Fourier series expansion; Periodic Riccati differential equations; Periodic Lyapunov differential equations; Periodic systems

Abstract:Combining Fourier series expansion with recursive matrix formulas, new reliable algorithms to compute the periodic, non-negative, definite stabilizing solutions of the periodic Riccati and Lyapunov matrix differential equations are proposed in this paper. First, periodic coefficients are expanded in terms of Fourier series to solve the time-varying periodic Riccati differential equation, and the state transition matrix of the associated Hamiltonian system is evaluated precisely with sine and cosine series. By introducing the Riccati transformation method, recursive matrix formulas are derived to solve the periodic Riccati differential equation, which is composed of four blocks of the state transition matrix. Second, two numerical sub-methods for solving Lyapunov differential equations with time-varying periodic coefficients are proposed, both based on Fourier series expansion and the recursive matrix formulas. The former algorithm is a dimension expanding method, and the latter one uses the solutions of the homogeneous periodic Riccati differential equations. Finally, the efficiency and reliability of the proposed algorithms are demonstrated by four numerical examples. (C) 2011 Elsevier B.V. All rights reserved.