Spectral Properties and Lyapunov Matrices of Primal - Dual Periodic Time-Delay systems, with Application to Balancing

被引：0

作者：

Gomez, Marco A. ^{[1
]}

Michiels, Wim ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Leuven, Belgium

来源：

IFAC PAPERSONLINE | 2020年 / 53卷 / 02期

关键词：

Delay systems; periodic systems; Lyapunov matrices; balancing; model reduction;

D O I：

10.1016/j.ifacol.2020.12.061

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In the paper we establish connections between the spectral properties of linear periodic systems with multiple delays with those of a dual system, obtained by transposition of the systems matrices and affine transformations of their arguments. The dual system also allows to introduce the dual Lyapunov matrix associated with the original system. We provide various energy interpretations of the primal-dual Lyapunov matrices, which allow us to generalize the concept of position balancing and explore its potential for model reduction. Copyright (C) 2020 The Authors.

引用

页码：4351 / 4356

页数：6

共 14 条

[1] [Anonymous], 1963, Differential-Difference Equations
[2] Butcher Eric A., 2013, Advances in Analysis and Control of Time-Delayed Dynamical Systems, P219
[3] On the Chebyshev spectral continuous time approximation for constant and periodic delay differential equations
Butcher, Eric A.
Bobrenkov, Oleg A.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (03) : 1541 - 1554
[4] Computation of the Lyapunov matrix for periodic time-delay systems and its application to robust stability analysis
Gomez, Marco A.
Egorov, Alexey V.
Mondie, Sabine
Zhabko, Alexey P.
[J]. SYSTEMS & CONTROL LETTERS, 2019, 132
[5] Halanay A., 1966, DIFFERENTIAL EQUATIO, V6
[6] Insperger T, 2004, ELEVENTH WORLD CONGRESS IN MECHANISM AND MACHINE SCIENCE, VOLS 1-5, PROCEEDINGS, P1816
[7] Insperger T, 2011, APPL MATH SCI, V178, P1, DOI 10.1007/978-1-4614-0335-7
[8] Insperger Tamas, 2000, Periodica Polytechnica, Mechanical Engineering, V44, P47
[9] Model reduction of time-delay systems using position balancing and delay Lyapunov equations
Jarlebring, Elias
Damm, Tobias
Michiels, Wim
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2013, 25 (02) : 147 - 166
[10] SOME H-OPTIMIZATION PROBLEMS FOR THE ITER PLASMA CONTROL SYSTEM
Zhabko, Natalia A.
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2009, 24 (05): : 1048 - 1056

← 1 2 →