Model Reduction of Time-Varying Systems

This paper presents new recursive projection techniques to compute reduced order models of time-varying linear systems. The methods produce a low rank approximation of the Gramians or of the Hankel map of the system and are mainly based on matrix operations that can exploit sparsity of the model. We show the practical relevance of our results with a few benchmark examples.

[1]  T. Kailath,et al.  On generalized balanced realizations , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[2]  John B. Moore,et al.  Toward time-varying balanced realization via Riccati equations , 1992, 1992 American Control Conference.

[3]  Henrik Sandberg,et al.  Balanced model reduction of linear time-varying systems , 2002 .

[4]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[5]  Sanjay Lall,et al.  Error-bounds for balanced model-reduction of linear time-varying systems , 2003, IEEE Trans. Autom. Control..

[6]  Peter Benner,et al.  Dimension Reduction of Large-Scale Systems , 2005 .

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

[8]  Paul Van Dooren,et al.  A collection of benchmark examples for model reduction of linear time invariant dynamical systems. , 2002 .

[9]  Kyle A. Gallivan,et al.  Sylvester equations and projection-based model reduction , 2004 .

[10]  Julián Salt,et al.  Periodic Optimal Control of Multirate Sampled Data Systems , 2001 .

[11]  Patrizio Colaneri,et al.  Periodic control systems , 2002 .

[12]  Paul Van Dooren,et al.  Estimating Gramians of Large-Scale Time-Varying Systems , 2002 .

[13]  Paul Van Dooren,et al.  Recursive Gramian and Hankel map approximation of large dynamical systems. , 2003 .

[14]  Gene H. Golub,et al.  Matrix computations , 1983 .

[15]  Recursive low rank Hankel approximation and model reduction , 2003, 2003 European Control Conference (ECC).

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

[17]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .

[18]  P. Dewilde,et al.  Time-Varying Systems and Computations , 1998 .

[19]  Leonard M. Silverman,et al.  Linear time-variable systems: Balancing and model reduction , 1983 .

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