This paper concerns the order reduction of single-input single-output (SISO) linear time-invariant continuous systems based on the impulse response Gramian. From the recursive relationship among the Gramians, a new formula is derived for computing the system matrix in controllability canonical form. The result is applied to the model reduction problem. Reduced models obtained approximate the reduced-order Gramians while preserving some initial time moments and Markov parameters of the original system.
Issue Section:
Technical Briefs
Keywords:
transient response,
continuous time systems,
iterative methods,
reduced order systems,
Markov processes,
matrix algebra
Topics:
Impulse (Physics)
1.
Agathoklis
, P.
, and Sreeram
, V.
, 1990, “Identification and Model Reduction From Impulse Response Data
,” Int. J. Control
0020-7179, 21
, pp. 1541
–1552
.2.
Sreeram
, V.
, and Agathoklis
, P.
, 1991, “Model Reduction of Linear Discrete Systems via Weighted Impulse Response Gramian
,” Int. J. Control
0020-7179, 53
, pp. 129
–144
.3.
Sreeram
, V.
, and Agathoklis
, P.
, 1993, “On the Computation of the Gram Matrix in Time Domain and its Application
,” IEEE Trans. Autom. Control
0018-9286, 38
, pp. 1516
–1520
.4.
Krajewski
, W.
, Lepschy
, A.
, and Viaro
, U.
, 1995, “Model Reduction by Matching Markov Parameters, Time Moments, and Impulse-Response Energies
,” IEEE Trans. Autom. Control
0018-9286, 40
, pp. 949
–953
.5.
Sreeram
, V.
, and Agathoklis
, P.
, 1992, “Discrete-System Reduction via Impulse-Response Gramians and its Relation to q-Markov Covers
.” IEEE Trans. Autom. Control
0018-9286, 37
, pp. 653
–658
.6.
Anderson
, B. D. O.
, and Skelton
, R. E.
, 1988, “The generation of all q-Markov Covers
,” IEEE Trans. Circuits Syst.
0098-4094, 35
, pp. 375
–384
.7.
Azou
, S.
, Brehonnet
, P.
, Vilbe
, P.
, and Calvez
, L. C.
, 2000, “A New Discrete Impulse Response Gramian and its Application to Model Reduction
,” IEEE Trans. Autom. Control
0018-9286, 45
, pp. 533
–537
.8.
Levit
, C.
, and Sreeram
, V.
, 1995, “Model Reduction via Parameter Matching Using a Gramian Technique
,” IEE Proc.: Control Theory Appl.
1350-2379, 142
, pp. 186
–196
.9.
Kailath
, T.
, 1980, Linear Systems
, Prentice-Hall
, New Jersey.10.
Sreeram
, V.
, and Yap
, F. K.
, 1991, “Characteristic Impulse-Response Gramian
,” Electron. Lett.
0013-5194, 27
, pp. 1285
–1287
.11.
Sreeram
, V.
, and Agathoklis
, P.
, 1994, “On the Properties of Gram Matrix
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
1057-7122, 41
, pp. 234
–237
.Copyright © 2006
by American Society of Mechanical Engineers
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