Dissipativity preserving model reduction by retention of trajectories of minimal dissipation

Mathematics of Control, Signals, and Systems

Volumn 21, Issue 3, 2009, Pages 171-201

  Trentelman, Harry L ^a   Minh, Ha Binh ^b   Rapisarda, Paolo ^c  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Viet Nam)

^c UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Behaviors; Driving variable representation; Minimal dissipation; Model reduction; Nevanlinna interpolation problem; Output nulling representations; Strictly dissipative systems

Indexed keywords

DRIVING VARIABLES; INTERPOLATION PROBLEMS; MODEL REDUCTION; NULLING; STRICTLY DISSIPATIVE;

ENERGY DISSIPATION; INTERPOLATION;

MATHEMATICAL MODELS;

EID: 72149127401     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-009-0043-6     Document Type: Article

References (32)

1. Antoulas AC (2004) Approximation of large-scale dynamical systems. SIAM Press, Philadelphia
2. AC Antoulas 2005 A new result on passivity-preserving model reduction Syst Control Lett 54 361 374 1129.93304 10.1016/j.sysconle.2004.07.007 2123709 (Pubitemid 40307811)
3. Belur MN (2003) Control in a behavioral context. Dissertation, University of Groningen
4. A Bultheel M van Baren 1986 Padé techniques for model reduction in linear system theory: a survey J Comp Appl Math 14 401 438 10.1016/0377- 0427(86)90076-2 (Pubitemid 16493546)
5. ∞ norm error bounds IEEE Trans Circuits Syst 42 1 23 29 0839.93024 10.1109/81.350793 1322383
6. S-Y Kim N Gopal LT Pillage 1994 Time-domain macromodels for VLSI interconnected analysis IEEE Trans Comput Aided Des Integr Circuit Syst 13 1257 1270 10.1109/43.317469
7. L Knockaert D de Zutter 1999 Passive reduced-order multiport modelling: the Padé-Laguerre, Krylov-Arnoldi-SVD connection Int J Electron Commun 53 254 260
8. ∞-error bounds Int J Control 39 1115 1193 0543.93036 10.1080/00207178408933239 748558
9. Minh HB (2009) Model reduction in a behavioral framework. Ph.D. Thesis, University of Groningen, The Netherlands
10. W Krajewski A Lepschy U Viaro 1994 Approximation of continuous-time linear systems using Markov parameters and energy indices IEEE Trans Autom Control 39 2126 2129 0925.93314 10.1109/9.328814 1295743
11. G Fanizza J Karlsson A Lindquist R Nagamune 2007 Passivity preserving model reduction by analytic interpolation Linear Algebra Appl 425 608 633 1125.93024 10.1016/j.laa.2007.03.014 2343059 (Pubitemid 47077794)
12. ∞ control. Ph.D. Thesis, University of Twente
13. BC Moore 1981 Principal components analysis in linear systems: controllability, observability, and model reduction IEEE Trans Autom Control AC-26 17 32 10.1109/TAC.1981.1102568
14. R Ober 1991 Balanced parametrization of classes of linear systems SIAM J Control Optim 29 1251 1287 0741.93010 10.1137/0329065 1132182
15. PC Opdenacker EA Jonckheere 1988 A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds IEEE Trans Circuits Syst 35 2 184 189 0659.93013 10.1109/31.1720 926005 (Pubitemid 18596694)
16. Polderman JW, Willems JC (1997) Introduction to mathematical system theory: a behavioral approach. Springer, Berlin
17. P Rapisarda JC Willems 1997 State maps for linear systems SIAM J Control Optim 35 3 1053 1091 0884.93006 10.1137/S0363012994268412 1444349
18. JM Schumacher 1988 Linear systems under external equivalence Linear Algebra Appl 102 1 33 0668.93019 10.1016/0024-3795(88)90318-7 941456
19. DC Sorensen 2005 Passivity preserving model reduction via interpolation of spectral zeros Syst Control Lett 54 347 360 1129.93340 10.1016/j.sysconle. 2004.07.006 2123708 (Pubitemid 40304804)
20. Trentelman HL, Willems JC (1991) The dissipation inequality and the algebraic Riccati equation. In: Bittanti S, Laub AJ, Willems JC(eds) The Riccati equation. Springer, Berlin
21. HL Trentelman JC Willems 1997 Every storage function is a state function Syst Control Lett 32 249 259 0902.93038 10.1016/S0167-6911(97)00081-9 1600194
22. Trentelman HL, Stoorvogel AA, Hautus MLJ (2001) Control theory for linear systems. Springer, London
23. Weiland S (1991) Theory of approximation and disturbance attenuation for linear system. Dissertation, University of Groningen
24. A Yousuff DA Wagie RE Skelton 1985 Linear system approximation via covariance equivalent realizations J Math Anal Appl 106 91 115 0573.93073 10.1016/0022-247X(85)90133-7 780321 (Pubitemid 15476175)
25. JM Wang C-C Chu Q Yu ES Kuh 2002 On projection-based algorithms for model-order reduction of interconnects IEEE Trans Circuits Syst I Fundam Theory Appl CAS-49 1564 1585 1945892
26. JC Willems 1983 Input-output and state-space representations of finite-dimensional linear time-invariant systems Linear Algebra Appl 50 581 608 0507.93017 10.1016/0024-3795(83)90070-8 699576
27. Willems JC, Trentelman HL (1991) The dissipation inequality and the algebraic Riccati equation. The Riccati equation. Springer, Berlin
28. JC Willems 1972 Dissipative dynamical systems-Part I: General theory Arch Ration Mech Anal 45 321 351 0252.93002 10.1007/BF00276493 527462
29. JC Willems 1972 Dissipative dynamical systems-Part II: Linear systems with quadratic supply rates Arch Ration Mech Anal 45 352 393 0252.93003 10.1007/BF00276494 527463
30. JC Willems HL Trentelman 1998 On quadratic differential forms SIAM J Control Optim 36 5 1703 1749 0912.93006 10.1137/S0363012996303062 1626821
31. JC Willems HL Trentelman 2002 Synthesis of dissipative systems using quadratic differential forms-Part I IEEE Trans Autom Control 47 1 53 69 10.1109/9.981722 1879690 (Pubitemid 34504322)
32. Zhou K (1996) Robust and optimal control. Prentice-Hall, New Jersey