References
[1]. Moore, B. C, (1981). “Principal Component Analysis in
Linear System: Controllability, Observability and Model
Reduction”. IEEE Transactions on Automatic Control,
Vol.26, pp.17-32.
[2]. Stewart, D.E and Leyk, T.S., (1996). “Error Estimates for
Krylov Subspace Approximations of Matrix Exponential”.
Journal on Computer and Applied Mathematics, Vol.72,
pp.359–369.
[3]. Y.V. Genin and S.Y. Kung, “A two-variable Approach to
the Model Reduction Problem with Hankel Norm Criterion”.
IEEE Transactions on Circuits and System, Vol. 28, No. 9, pp.
912-924.
[4]. Sirovich, L, (1987). “Turbulence and the Dynamics of
Coherent Structures”. Quarterly of Applied Mathematics,
Vol.5, pp.561–590.
[5]. Saad, Y., (1992). “Analysis of Some Krylov Subspace
Approximations to the Matrix Exponential Operator”. SIAM
Journal on Numerical Analysis, Vol.29, pp. 209-228.
[6]. Gugercin, S., Antoulas, A.C., and Beattie, C.A., (2006).
“A Rational Krylov Iteration for Optimal H2 Model
th Reduction”. Proceedings of the 17 International
Symposium on Mathematical Theory of Networks and
Systems, pp.1665-1667.
[7]. Y. –F. Su, J, Wang, X, Zeng, Z Bai, Charles Chiang and D.
Zhou, (2004). “SAPOR: Second-Order Arnoldi Method for
Passive Order Reduction of RCS Circuits”. Proceedings of
IEEE International Conference on Computer Aided Design.
[8]. Y. Chahlaoui, and P. Van Dooren, (2002). “A Collection
of Benchmark Examples for Model Reduction of Linear Time
Invariant Dynamical Systems”. Retrived from
http://citeseerx.ist.psu.edu/viewdoc/download?doi=
10.1.1.546.9783&rep=rep1&type=pdf
[9]. Anderson, B. D. O., and Vongpanitlerd, S., (1973).
Network Analysis and Synthesis. Englewood Cliffs, NJ:
Prentice-Hall.
[10]. Antoulas, A. C. (2003). Lectures on the Approximation
of Linear Dynamical Systems. Draft, to appear, SIAM Press.
[11]. Antoulas, A. C., (1998). ”Approximation of Linear
Operators in the 2-norm”. Special Issue of LAA (Linear
Algebra and Applications) on Challenges in Matrix Theory,
Vol.278, pp.309–316.
[12]. Antoulas, A. C., Sorensen, D. C., and Gugercin, S.,
(2001). “A Survey of Model Reduction Methods for Large
Scale Systems”. Contemporary Mathematics, AMS
Publications, Vol.28, pp. 193-219.
[13]. Antoulas, A. C., and Sorensen, D. C., (2002). “The
Sylvester Equation and Approximate Balanced Reduction”.
Fourth Special Issue on Linear Systems and Control, Linear
Algebra and Its Applications, pp.351–352.
[14]. Benner, P., E., Quintana-Orti, E. S. and Quintana-Orti,
G., (2001). “Efficient Numerical Algorithms for Balanced
Stochastic Truncation”. International Journal of Applied
Mathematics and Computer Science, Special Issue:
Numerical Analysis and Systems Theory, Vol. 11, No. 5.
[15]. Antoulas, A. C., Sorensen, D. C., and Zhou, Y. K.,
(2002). “On the decay rate of Hankel Singular Values and
Related Issues”. Systems and Control Letters, Vol. 46,
pp.323–342.
[16]. Enns, D., (1984). “Model Reduction with Balanced
Realizations: An Error Bound and a Frequency Weighted
rd Generalization”. Proceedings of the 23 IEEE Conference
Decision and Control.
[17]. Green, M., (1981). “A Relative Error Bound for
Balanced Stochastic Truncation”. IEEE Transactions on
Automatic Control, Vol. 33.
[18]. Gawronski, W., and Juang, J. N., (1990). “Model
Reduction in Limited Time and Frequency Intervals”.
International Journal on Systems Science, Vol. 21, No. 2, pp. 349-376.
[19]. Green, M., (1988). “A Relative Error Bound for
Balanced Stochastic Truncation”. IEEE Transactions on
Automatic Control, pp.961–965.
[20]. Pernebo, L., and Silverman, L. M., (1982). ”Model
Reduction via Balanced State Space Representation”. IEEE
Transactions on Automatic Control, pp.382–382.
[21]. Zhou, K., Doyle, J. C., and Glover, K., (1996). Robust
and Optimal Control. Engelwood Cliffs, NJ: Prentice Hall.
[22]. Gugercin, S., and Antoulas, A. C., (2000). “A
Comparative Study of 7 Model Reduction Algorithms”.
Proceedings of IEEE International Conference on Decision
and Control.
[23]. Lin, C. A., and Chiu, T. Y., (1992). “Model Reduction via
Frequency Weighted Balanced Realization”. Control
Theory and Advanced Technology, Vol. 8, pp. 341-351.
[24]. Wang, G., Sreeram, V., and Liu, W. Q., (1999). “A New
Frequency Weighted Balanced Truncation Method and an
Error Bound”. IEEE Transactions on Automatic Control, Vol.
44, No. 9, pp. 1734-1737.
[25]. Wang, W., and Safanov, M. G., (1992). ”Multiplicativeerror
Bound for Balanced Stochastic Truncation Model
Reduction”. IEEE Transactions on Automatic Control, Vol.
37, No. 8, pp. 1265-1267.
[26]. Ober, R., (1991). “Balanced Parameterization of
Classes of Linear Systems”. SIAM Journal on Control
Applications.
[27]. Opdenacker, P. C., and Jonckheere, E. A., (1988). “A
Contraction Mapping Preserving Balanced Reduction
Scheme and its Infinity Norm Error Bounds”. IEEE
Transactions on Circuits and Systems.
[28]. Jonckheere, E. A., and Silverman, L. M., (1983). “A
New of Invariants for Linear System Application to Reduced
Order Compensator Designs”. IEEE Transactions on
Automatic Control, Vol.28, pp.953-964.
[29]. Liu, Y., and Anderson, B.D.O., (1989). “Singular
Perturbation Approximation of Balanced System”.
International Journal of Control, Vol.50, pp.1379–140.
[30]. Sreeram, V., Anderson, B. D. O., and Madievski, A. G.,
(1995). “Frequency Weighted Balanced Reduction Technique: Generalization and an Error Bound”. in
Proceedings of 34 IEEE Conference on Decision and
Control, New Orleans, Louisiana, USA.
[31]. J. Li, F. Wang, and J. White, (1999). “An Efficient
Lyapunov Equation-based Approach for Generating
Reduced-order Models of Interconnect”. Proceedings of
36 IEEE/ACM Design Automation Conference, New
Orleans, LA.
[32]. T. Penzl, (2000). “Eigen values Decay Bounds for
Solutions of Lyapunov Equation the Symmetric Case”. Systems and Control Letters.
[33]. Kumar. A, and Chandra. D., (2014). “Improved Padepole
Clustering Approximant”. International Journal of
Computer Applications, Vol.114, No.1, pp. 28-32.
[34]. Gupta. D, and Kumar. A., (2015). “An Investigation into
Model Order Reduction through Balancing Methods and
their Error Norm”. International Journal Engineering
Technology and Advanced Engineering, Vol. 6, No.3,
pp.287-292.