A time-limited balanced reduction method

In this paper, we introduce a time-limited balanced reduction method based on time-domain representations of the system gramians. The method guarantees stability and yields a simple /spl Hscr/;/sub /spl infin// error bound. A numerical example is illustrated to examine the efficiency of the proposed method.

[1]  Serkan Gugercin,et al.  A survey of balancing methods for model reduction , 2003, 2003 European Control Conference (ECC).

[2]  U. Desai,et al.  A transformation approach to stochastic model reduction , 1984 .

[3]  A. Antoulas,et al.  A comparative study of 7 algorithms for model reduction , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[4]  G. Wang,et al.  A new frequency-weighted balanced truncation method and an error bound , 1999, IEEE Trans. Autom. Control..

[5]  Paul Van Dooren,et al.  On some recent developments in projection-based model reduction , 1998 .

[6]  Ching-An Lin,et al.  Model Reduction via Frequency Weighted Balanced Realization , 1990, 1990 American Control Conference.

[7]  D. Enns Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[8]  B. Anderson,et al.  Frequency weighted balanced reduction technique: a generalization and an error bound , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[9]  Danny C. Sorensen,et al.  A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations , 2004, Numerical Algorithms.

[10]  R. Ober Balanced parametrization of classes of linear systems , 1991 .

[11]  Michael Green,et al.  Balanced stochastic realizations , 1988 .

[12]  Paul Van Dooren,et al.  A rational Lanczos algorithm for model reduction , 1996, Numerical Algorithms.

[13]  A. Varga,et al.  On stochastic balancing related model reduction , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[14]  M. Green,et al.  A relative error bound for balanced stochastic truncation , 1988 .

[15]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[16]  E. Jonckheere,et al.  A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds , 1988 .

[17]  Michael G. Safonov,et al.  Multiplicative-error bound for balanced stochastic truncation model reduction , 1992 .

[18]  B. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[19]  Edmond A. Jonckheere,et al.  A new set of invariants for linear systems--Application to reduced order compensator design , 1983 .

[20]  Enrique S. Quintana-Ortí,et al.  Efficient numerical algorithms for balanced stochastic truncation , 2001 .

[21]  Jer-Nan Juang,et al.  Model reduction in limited time and frequency intervals , 1990 .

[22]  Kemin Zhou,et al.  Frequency-weighted 𝓛∞ norm and optimal Hankel norm model reduction , 1995, IEEE Trans. Autom. Control..