Model reduction by moment matching, steady-state response and projections

The model reduction problem by moment matching for linear systems is revisited and connections between projection based methods and the notion of steady-state response are established. A systems theoretic interpretation of the (oblique) projectors used in Krylov methods is derived and a new family of reduced order models achieving moment matching is given. Finally, the equivalence between various families of reduced order models, all achieving moment matching, is established.

[1]  W. Steven Gray,et al.  General input balancing and model reduction for linear and nonlinear systems , 1997, 1997 European Control Conference (ECC).

[2]  Paul Van Dooren,et al.  Model reduction and the solution of Sylvester equations , 2006 .

[3]  Tryphon T. Georgiou,et al.  A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint , 2001, IEEE Trans. Autom. Control..

[4]  D. Meyer.  Fractional balanced reduction: model reduction via fractional representation , 1990 .

[5]  J. Willems,et al.  On the solution of the minimal rational interpolation problem , 1990 .

[6]  M. Kreĭn,et al.  ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM , 1971 .

[7]  C. Byrnes,et al.  A complete parameterization of all positive rational extensions of a covariance sequence , 1995, IEEE Trans. Autom. Control..

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

[9]  M. Safonov,et al.  Optimal Hankel model reduction for nonminimal systems , 1990 .

[10]  Serkan Gugercin,et al.  Interpolation theory for structure-preserving model reduction , 2008, 2008 47th IEEE Conference on Decision and Control.

[11]  Alessandro Astolfi,et al.  A note on model reduction by moment matching for nonlinear systems , 2010 .

[12]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[13]  Alessandro Astolfi,et al.  Model Reduction by Moment Matching for Linear and Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

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

[15]  Tryphon T. Georgiou,et al.  The interpolation problem with a degree constraint , 1999, IEEE Trans. Autom. Control..

[16]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.