SPECTRAL FACTORIZATION BY SYMMETRIC EXTRACTION FOR DISTRIBUTED PARAMETER SYSTEMS

作     者：Winkin, J. J. Callier, F. M. Jacob, B. Partington, J. R. 

作者机构：Univ Namur FUNDP Dept Math B-5000 Namur Belgium Univ Dortmund Fachbereich Math D-44221 Dortmund Germany Univ Leeds Sch Math Leeds LS2 9JT W Yorkshire England 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：2005年第43卷第4期

页      面：1435-1466页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：distributed parameter systems spectral factorization coercivity meromorphic function entire function finite order infinite product symmetric extraction convergence analysis 

摘      要：The spectral factorization problem of a scalar coercive spectral density is considered in the framework of the Callier-Desoer algebra of distributed parameter system transfer functions. Criteria are given for the infinite product representation of a meromorphic coercive spectral density of finite order and for the convergence of infinite product representations of spectral factors, i.e., for the convergence of the symmetric extraction method for solving the spectral factorization problem of such spectral density. These convergence criteria are applied to the solution of the linear-quadratic optimal control problem by spectral factorization for a specific class of semigroup Hilbert state-space systems with a Riesz-spectral generator. The speed of convergence of the symmetric extraction method is also considered. As an example a damped vibrating string model is handled.