Abstract
In this paper, the model reduction problem of neutral systems with time-varying delays is studied with suboptimality under the measure. A delay-dependent bounded realness condition of the norm is given via linear matrix inequalities (LMIs). Based on such a condition, a sufficient condition to characterize the existence of the reduced-order models is given in terms of LMIs with inverse constraints. By employing a sequential convex optimization approach, a reduced-order model can be computed with error less than some prescribed scalar .
Issue Section:
Technical Briefs
1.
Grigoriadis
, K. M.
, 1995, “Optimal H∞ Model Reduction via Linear Matrix Inequalities: Continuous- and Discrete-Time Cases
,” Syst. Control Lett.
0167-6911, 26
(5
), pp. 321
–333
.2.
Xu
, S.
, Lam
, J.
, Huang
, S.
, and Yang
, C.
, 2001, “H∞ Model Reduction for Linear Time-Delay Systems: Continuous-Time Case
,” Int. J. Control
0020-7179, 74
(11
), pp. 1062
–1074
.3.
El Ghaoui
, L.
, Oustry
, F.
, and AitRami
, M.
, 1997, “A Cone Complementarity Linearization Algorithm for Static Output-Feedback and Related Problems
,” IEEE Trans. Autom. Control
0018-9286, 42
(8
), pp. 1171
–1176
.4.
Han
, Q.-L.
, 2002, “Robust Stability of Uncertain Delay-Differential Systems of Neutral Type
,” Automatica
0005-1098, 38
(4
), pp. 719
–723
.5.
Niculescu
, S.-I.
, 2001, “On Delay-Dependent Stability Under Model Transformations of Some Neutral Linear Systems
,” Int. J. Control
0020-7179, 74
(6
), pp. 609
–617
.6.
Wang
, Z.
, Lam
, J.
, and Burnham
, K. J.
, 2002, “Stability Analysis and Observer Design for Neutral Delay System
,” IEEE Trans. Autom. Control
0018-9286, 47
(3
), pp. 478
–483
.7.
Bliman
, P. A.
, 2002, “Lyapunov Equation for the Stability of Linear Delay Systems of Retarded and Neutral Type
,” IEEE Trans. Autom. Control
0018-9286, 47
(2
), pp. 327
–335
.8.
Park
, J. H.
, 2002, “Stability Criterion for Neutral Differential Systems With Mixed Multiple Time-Varying Delay Arguments
,” Math. Comput. Simul.
0378-4754, 59
(5
), pp. 401
–412
.9.
Xu
, S.
, Lam
, J.
, and Yang
, C.
, 2001, “H∞ and Positive Real-Control for Linear Neutral Delay Systems
,” IEEE Trans. Autom. Control
0018-9286, 46
(8
), pp. 1321
–1326
.10.
Lee
, Y. S.
, Moon
, Y. S.
, Kwon
, W. H.
, and Lee
, K. H.
, 2001, “Delay-Dependent Robust H∞ Control for Uncertain Systems With Time-Varying State-Delay
,” Proceedings of 40th Conference on Decision and Control
, IEEE
, Orlando, FL
, pp. 3208
–3213
.11.
Mahmoud
, M. S.
, and Zribi
, M.
, 1999, “H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities
,” J. Optim. Theory Appl.
0022-3239, 100
(1
), pp. 89
–122
.12.
Wang
, H.
, Lam
, J.
, Xu
, S.
, and Huang
, S.
, 2002, “Robust H∞ Reliable Control for a Class of Uncertain Neutral Delay Systems
,” Int. J. Syst. Sci.
0020-7721, 33
(3
), pp. 611
–622
.13.
Skelton
, R. E.
, Iwasaki
, T.
, and Grigoriadis
, K. M.
, 1998, A Unified Algebraic Approach to Linear Control Design
, Taylor & Francis
, London.14.
Gahinet
, P.
, and Apkarian
, P.
, 1994, “A Linear Matrix Inequality Approach to H∞ Control
,” Int. J. Robust Nonlinear Control
1049-8923, 4
, pp. 421
–448
.15.
de Oliveira
, M. C.
, and Geromel
, J. C.
, 1997, “Numerical Comparison of Output Feedback Design Methods
,” Proceedings of American Control Conference
, American Automatic Control Council
, Albuquerque, NM
, pp. 72
–76
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.