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Volumn 25, Issue 2, 2013, Pages 147-166

Model reduction of time-delay systems using position balancing and delay Lyapunov equations

Author keywords

Balanced truncation; Lyapunov equations; Model reduction; Time delay systems

Indexed keywords

BALANCED TRUNCATION; CO-ORDINATE TRANSFORMATION; CONTROLLABILITY AND OBSERVABILITIES; LINEAR TIME-DELAY SYSTEM; LYAPUNOV EQUATION; MODEL ORDER REDUCTION; MODEL REDUCTION; TIME-DELAY SYSTEMS;

EID: 84882664013     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-012-0096-9     Document Type: Article
Times cited : (45)

References (36)
  • 2
    • 0010011201 scopus 로고    scopus 로고
    • A survey of model reduction methods for large-scale systems
    • 1850408 10.1090/conm/280/04630
    • Antoulas A, Sorensen D, Gugercin S (2001) A survey of model reduction methods for large-scale systems. Contemp Math 280:193-219
    • (2001) Contemp Math , vol.280 , pp. 193-219
    • Antoulas, A.1    Sorensen, D.2    Gugercin, S.3
  • 3
    • 84976855597 scopus 로고
    • Solution of the matrix equation AX+XB=C
    • 10.1145/361573.361582
    • Bartels R, Stewart GW (1972) Solution of the matrix equation AX+XB=C. Comm ACM 15(9):820-826
    • (1972) Comm ACM , vol.15 , Issue.9 , pp. 820-826
    • Bartels, R.1    Stewart, G.W.2
  • 4
    • 58249141852 scopus 로고    scopus 로고
    • Interpolatory projection methods for structure-preserving model reduction
    • 2494198 1159.93317 10.1016/j.sysconle.2008.10.016
    • Beattie C, Gugercin S (2009) Interpolatory projection methods for structure-preserving model reduction. Syst Control Lett 58(3):225-232
    • (2009) Syst Control Lett , vol.58 , Issue.3 , pp. 225-232
    • Beattie, C.1    Gugercin, S.2
  • 6
    • 79953205915 scopus 로고    scopus 로고
    • Efficient balancing based MOR for large scale second order systems
    • 2784464 1221.93039 10.1080/13873954.2010.540822
    • Benner P, Saak J (2011) Efficient balancing based MOR for large scale second order systems. Math Comput Model Dyn Syst 17(2):123-143
    • (2011) Math Comput Model Dyn Syst , vol.17 , Issue.2 , pp. 123-143
    • Benner, P.1    Saak, J.2
  • 10
    • 79951609481 scopus 로고    scopus 로고
    • Krylov subspace methods for linear infinite-dimensional systems
    • 2761118 10.1109/TAC.2010.2090063
    • Harkort C, Deutscher J (2011) Krylov subspace methods for linear infinite-dimensional systems. IEEE Trans Autom Control 56(2):441-447
    • (2011) IEEE Trans Autom Control , vol.56 , Issue.2 , pp. 441-447
    • Harkort, C.1    Deutscher, J.2
  • 11
    • 80051518379 scopus 로고    scopus 로고
    • Polynomial approximations of the Lyapunov matrix of a class of time delay systems
    • Sinaia, Romania
    • Huesca E, Mondié S, Santos J (2009) Polynomial approximations of the Lyapunov matrix of a class of time delay systems. In: Proceedings of the 8th IFAC workshop on time-delay systems, Sinaia, Romania
    • (2009) Proceedings of the 8th IFAC Workshop on Time-delay Systems
    • Huesca E, M.1
  • 12
    • 79953799459 scopus 로고    scopus 로고
    • Characterizing and computing the cal H2 norm of time-delay systems by solving the delay Lyapunov equation
    • Jarlebring E, Vanbiervliet J, Michiels W (2011) Characterizing and computing the H2 norm of time-delay systems by solving the delay Lyapunov equation. IEEE Trans Autom Control 56(4):814-825
    • (2011) IEEE Trans Autom Control , vol.56 , Issue.4 , pp. 814-825
    • Jarlebring, E.1    Vanbiervliet, J.2    Michiels, W.3
  • 13
    • 0346895349 scopus 로고    scopus 로고
    • Lyapunov-Krasovskii functionals for scalar time delay equations
    • 2027468 1157.34354 10.1016/S0167-6911(03)00221-4
    • Kharitonov V (2004) Lyapunov-Krasovskii functionals for scalar time delay equations. Syst Control Lett 51(2):133-149
    • (2004) Syst Control Lett , vol.51 , Issue.2 , pp. 133-149
    • Kharitonov, V.1
  • 14
    • 27944453519 scopus 로고    scopus 로고
    • Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: A single delay case
    • 2152637 1097.93027 10.1080/00207170500164837
    • Kharitonov V (2005) Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case. Int J Control 78(11):783-800
    • (2005) Int J Control , vol.78 , Issue.11 , pp. 783-800
    • Kharitonov, V.1
  • 15
    • 33646138476 scopus 로고    scopus 로고
    • Lyapunov matrices for a class of time delay systems
    • 2225371 1129.34331 10.1016/j.sysconle.2006.01.006
    • Kharitonov V (2006) Lyapunov matrices for a class of time delay systems. Syst Control Lett 55(7):610-617
    • (2006) Syst Control Lett , vol.55 , Issue.7 , pp. 610-617
    • Kharitonov, V.1
  • 16
    • 7444270647 scopus 로고    scopus 로고
    • Exponential estimates for time delay systems
    • 2097797 1157.34355 10.1016/j.sysconle.2004.05.016
    • Kharitonov V, Hinrichsen D (2004) Exponential estimates for time delay systems. Syst Control Lett 53(5):395-405
    • (2004) Syst Control Lett , vol.53 , Issue.5 , pp. 395-405
    • Kharitonov, V.1    Hinrichsen, D.2
  • 17
    • 33745615787 scopus 로고    scopus 로고
    • Lyapunov matrices for time-delay systems
    • 2245441 1100.93045 10.1016/j.sysconle.2006.01.005
    • Kharitonov V, Plischke E (2006) Lyapunov matrices for time-delay systems. Syst Control Lett 55(9):697-706
    • (2006) Syst Control Lett , vol.55 , Issue.9 , pp. 697-706
    • Kharitonov, V.1    Plischke, E.2
  • 18
    • 0037210861 scopus 로고    scopus 로고
    • Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems
    • 2136548 1014.93031 10.1016/S0005-1098(02)00195-4
    • Kharitonov V, Zhabko AP (2003) Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica 39(1):15-20
    • (2003) Automatica , vol.39 , Issue.1 , pp. 15-20
    • Kharitonov, V.1    Zhabko, A.P.2
  • 19
    • 0345102509 scopus 로고    scopus 로고
    • Laguerre and Kautz shift approximations of delay systems
    • 0963.93042 10.1080/002071799220678
    • Mäkilä P, Partington J (1999) Laguerre and Kautz shift approximations of delay systems. Int J Control 72(10):932-946
    • (1999) Int J Control , vol.72 , Issue.10 , pp. 932-946
    • Mäkilä, P.1    Partington, J.2
  • 20
    • 17144472049 scopus 로고    scopus 로고
    • Shift operator induced approximations of delay systems
    • 1720144 0935.93047 10.1137/S0363012998339678
    • Mäkilä P, Partington J (1999) Shift operator induced approximations of delay systems. SIAM J Control Optim 37(6):1897-1912
    • (1999) SIAM J Control Optim , vol.37 , Issue.6 , pp. 1897-1912
    • Mäkilä, P.1    Partington, J.2
  • 21
    • 85055789488 scopus 로고
    • Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spaces
    • Mastinšek M (1994) Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spaces. Acta Math Univ Comen LXIII 2:193-206
    • (1994) Acta Math Univ Comen LXIII , vol.2 , pp. 193-206
    • Mastinšek, M.1
  • 22
    • 0030285070 scopus 로고    scopus 로고
    • Balancing and model reduction for second-order form linear systems
    • 1419687 0859.93015 10.1109/9.544000
    • Meyer DG, Srinivasan S (1996) Balancing and model reduction for second-order form linear systems. IEEE Trans Autom Control 41(11):1632-1644
    • (1996) IEEE Trans Autom Control , vol.41 , Issue.11 , pp. 1632-1644
    • Meyer, D.G.1    Srinivasan, S.2
  • 24
    • 84856295301 scopus 로고    scopus 로고
    • Krylov-based model order reduction of time-delay systems
    • 2869491 1247.65086 10.1137/100797436
    • Michiels W, Jarlebring E, Meerbergen K (2011) Krylov-based model order reduction of time-delay systems. SIAM J Matrix Anal Appl 32(4):1399-1421
    • (2011) SIAM J Matrix Anal Appl , vol.32 , Issue.4 , pp. 1399-1421
    • Michiels, W.1    Jarlebring, E.2    Meerbergen, K.3
  • 28
    • 0041568115 scopus 로고
    • Schur complements and statistics
    • 604341 0455.15012 10.1016/0024-3795(81)90232-9
    • Ouellette DV (1981) Schur complements and statistics. Linear Algebra Appl 36:187-295
    • (1981) Linear Algebra Appl , vol.36 , pp. 187-295
    • Ouellette, D.V.1
  • 29
    • 78651256007 scopus 로고    scopus 로고
    • Model reduction of delay systems
    • V. Blondel A. Megretski (eds) Princeton university press Princeton
    • Partington J (2004) Model reduction of delay systems. In: Blondel V, Megretski A (eds) Unsolved problems in mathematical systems and control theory. Princeton university press, Princeton, pp 29-32
    • (2004) Unsolved Problems in Mathematical Systems and Control Theory , pp. 29-32
    • Partington, J.1
  • 31
    • 53349089857 scopus 로고    scopus 로고
    • Balanced truncation model reduction of second-order systems
    • 2449500 1151.93010 10.1080/13873950701844170
    • Reis T, Stykel T (2008) Balanced truncation model reduction of second-order systems. Math Comput Model Dyn Syst 14(5):391-406
    • (2008) Math Comput Model Dyn Syst , vol.14 , Issue.5 , pp. 391-406
    • Reis, T.1    Stykel, T.2
  • 32
    • 81055156812 scopus 로고    scopus 로고
    • On dominant poles and model reduction of second order time-delay systems
    • 2856060 1236.93080 10.1016/j.apnum.2011.09.005
    • Saadvandi M, Meerbergen K, Jarlebring E (2012) On dominant poles and model reduction of second order time-delay systems. Appl Numer Math 62(1):21-34
    • (2012) Appl Numer Math , vol.62 , Issue.1 , pp. 21-34
    • Saadvandi, M.1    Meerbergen, K.2    Jarlebring, E.3
  • 33
    • 79952911825 scopus 로고    scopus 로고
    • Using spectral discretisation for the optimal H2 design of time-delay systems
    • Vanbiervliet J, Michiels W, Jarlebring E (2011) Using spectral discretisation for the optimal H2 design of time-delay systems. Int J Control 84(2):228-241
    • (2011) Int J Control , vol.84 , Issue.2 , pp. 228-241
    • Vanbiervliet, J.1    Michiels, W.2    Jarlebring, E.3
  • 34
    • 57249089086 scopus 로고    scopus 로고
    • Lyapunov-Krasovskii functionals for scalar neutral type time delay equation
    • Velázquez-Velázquez J, Kharitonov V (2009) Lyapunov-Krasovskii functionals for scalar neutral type time delay equation. Syst Control Lett 58(1):17-25
    • (2009) Syst Control Lett , vol.58 , Issue.1 , pp. 17-25
    • Velázquez-Velázquez, J.1    Kharitonov, V.2
  • 35
  • 36
    • 21144480202 scopus 로고
    • Contragredient transformations applied to optimal projection equations
    • 1223476 10.1016/0024-3795(93)90484-6
    • Zigic D, Watson L, Beattie C (1993) Contragredient transformations applied to optimal projection equations. Linear Algebra Appl 188-189:665-676
    • (1993) Linear Algebra Appl , vol.188-189 , pp. 665-676
    • Zigic, D.1    Watson, L.2    Beattie, C.3


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