Solving periodic Lyapunov matrix equations via finite steps iteration

被引：25

作者：

Cai, G. -B. ^{[1
]}

Hu, C. -H. ^{[1
]}

机构：

[1] Xian Res Inst High Tech, Dept Automat, Xian 710025, Shaanxi, Peoples R China

来源：

IET CONTROL THEORY AND APPLICATIONS | 2012年 / 6卷 / 13期

关键词：

POLE ASSIGNMENT; SYSTEMS; ALGORITHMS; STABILIZATION; FORM;

D O I：

10.1049/iet-cta.2011.0560

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Periodic Lyapunov matrix equations play important roles in stability analysis and stabilisation of discrete-time periodic systems. In this paper, an iterative algorithm for solving periodic Lyapunov matrix equations is established. It is shown that the proposed iteration converges to the unique solution of the considered matrix equations at finite steps with arbitrary initial condition despite the stability of the associated discrete-time periodic linear systems. Both the reverse-time and forward-time discrete-time periodic Lyapunov matrix equations are considered. Numerical examples are worked out to illustrate the effectiveness of the proposed algorithm.

引用

页码：2111 / 2119

页数：9

共 33 条

[1]

[Anonymous], 1995, OPTIMAL SAMPLED DATA, DOI DOI 10.1007/978-1-4471-3037-6

[2] SOLUTION OF THE DISCRETE-TIME LYAPUNOV MATRIX EQUATION IN CONTROLLABLE CANONICAL FORM [J].

BITMEAD, RR .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1979, 24 (03) :481-482

[3] THE SIMPLE PENDULUM AND THE PERIODIC LQG CONTROL PROBLEM [J].

BITTANTI, S ;

HERNANDEZ, DB ;

ZERBI, G .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1991, 328 (2-3) :299-315

[4]

Bittanti S., 1996, CONTROL DYNAMIC SYST, V78, P313

[5]

BOJANCZYK A, 1992, P SOC PHOTO-OPT INS, V1770, P31, DOI 10.1117/12.130915

[6]

Byers R., 1995, TECHNICAL REPORTS U

[7] Closed-form solution of particular case of algebraic Riccati equation using Moser-Veselov equation [J].

Choi, Y. ;

Park, J. ;

Lee, S. .

IET CONTROL THEORY AND APPLICATIONS, 2010, 4 (05) :865-870

[8] Efficient iterative method for solving the second-order Sylvester matrix equation EVF2-AVF-CV=BW [J].

Dehghan, M. ;

Hajarian, M. .

IET CONTROL THEORY AND APPLICATIONS, 2009, 3 (10) :1401-1408

[9] Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations [J].

Dehghan, Mehdi ;

Hajarian, Masoud .

APPLIED MATHEMATICAL MODELLING, 2011, 35 (07) :3285-3300

[10] The general coupled matrix equations over generalized bisymmetric matrices [J].

Dehghan, Mehdi ;

Hajarian, Masoud .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (06) :1531-1552

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