Stability-preserving parametric model reduction by matrix interpolation

References

• Weile , D.S. , Michielssen , E. , Grimme , E. and Gallivan , K. 1999 . A method for generating rational interpolant reduced order models of two-parameters linear systems . Appl. Math. Lett , 12 : 93 – 102 .
   Web of Science ®Google Scholar
• Daniel , L. , Siong , O. , Lee , K. and White , J. 2004 . A multiparameter moment matching model reduction approach for generating geometrically parameterized interconnect performance models . IEEE Trans. Comput. Aided Des. Integr. Circuits Syst , 5 : 678 – 693 .
   Google Scholar
• Leung , A.T. and Khazaka , R. 2005 . Parametric model order reduction technique for design optimization . Proc. Intl. Symp. Circuits Syst. 2 , : 1290 – 1293 .
   Google Scholar
• Peng , L. , Liu , F. , Pileggi , L.T. and Nassif , S.R. 2005 . Modeling interconnect variability using efficient parametric model order reduction , 958 – 963 . Munich, , Germany : Proceedings of the Design, Automation and Test In Europe Conference and Exhibition .
   Google Scholar
• Baur , U. and Benner , P. 2009 . Modellreduktion für parametrisierte Systeme durch balanciertes Abschneiden und Interpolation . Automatisierungstechnik , 57 : 411 – 419 .
   Web of Science ®Google Scholar
• Baur , U. , Beattie , C. , Benner , P. and Gugercin , S. November 2009 . Interpolatory Projection Methods for Parameterized Model Reduction , November , Chemnitz, , Germany : Chemnitz Scientific Computing Preprints 09-08 . TU Chemnitz
   Google Scholar
• Panzer , H. , Mohring , J. , Eid , R. and Lohmann , B. 2010 . Parametric model order reduction by matrix interpolation . Automatisierungstechnik , 58 : 475 – 484 .
   Web of Science ®Google Scholar
• Lohmann , B. and Eid , R. 2009 . “ Efficient order reduction of parametric and nonlinear models by superposition of locally reduced models ” . In Methoden und Anwendungen der Regelungstechnik , Edited by: Roppencker und , G. and Lohmann , B. 27 – 37 . Erlangen-Münchener Workshops 2007/2008, Shaker Verlag, Aachen . Hrsg.,
   Google Scholar
• B. Lohmann and R. Eid, A new framework for order reduction of parametric models by superposition of locally reduced ones, Presented at the Workshop on Model Reduction of Parametrized Systems, MoRePas 09, Münster, September 2009. www.rt.mw.tum.de (http://www.rt.mw.tum.de) (Accessed: 15 April 2010 ).
   Google Scholar
• Bai , Z. , Feldmann , P. and Freund , R. 1997 . Stable and passive reduced-order models based on partial Padé approximation via the Lanczos process , Murray Hill, NJ : Bell Laboratories, Lucent Technologies . Numerical Analysis Manuscript 97/3–10
   Google Scholar
• Grimme , E. , Sorensen , D. and Van Dooren , P. 1995 . Model reduction of state space systems via an implicitly restarted Lanczos method . Numer. Algorithm , 12 : 1 – 31 .
   Google Scholar
• Jaimoukha , I.M. and Kasenally , E.M. 1997 . Implicitly restarted Krylov subspace methods for stable partial realizations . SIAM J. Matrix Anal. Appl , 18 : 633 – 652 .
   Web of Science ®Google Scholar
• Antoulas , A. 2005 . A new result on passivity preserving model reduction . Syst. Control Lett , 54 : 361 – 374 .
   Google Scholar
• Sorensen , D.C. 2005 . Passivity preserving model reduction via interpolation of spectral zeros . Syst. Control Lett , 54 : 347 – 360 .
   Web of Science ®Google Scholar
• Ionutiu , R. , Rommes , J. and Antoulas , A.C. 2008 . Passivity-preserving model reduction using dominant spectral-zero interpolation . IEEE Trans. Comput. Aided Des. Integr. Circuits Syst , 27 December : 2250 – 2263 .
   Google Scholar
• Villemagne , C.D. and Skelton , R.E. 1987 . Model reduction using a projection formulation . Int. J. Control , 46 : 2141 – 2169 .
   Web of Science ®Google Scholar
• Gugercin , S. and Antoulas , A. 2006 . Model reduction of large-scale systems by least squares . Linear Algebra Appl , 415 : 290 – 321 .
   Web of Science ®Google Scholar
• Yousefi , A. 2006 . Preserving stability in model and controller reduction with application to embedded systems , München : Ph.D. thesis, Institute of Automatic Control, Technische Universität .
   Google Scholar
• Castañé-Selga , R. , Lohmann , B. and Eid , R. 2010 . Stability preservation in projection-based model order reduction of large scale systems . submitted to Eur. J. Control ,
   Google Scholar
• Antoulas , A.C. 2005 . Approximation of Large-Scale Dynamical Systems , Philadelphia, PA : SIAM .
   Google Scholar
• Freund , R.W. 2003 . Model reduction methods based on krylov subspaces . Acta Numerica , 12 : 267 – 319 .
   Google Scholar
• Grimme , E.J. 1997 . Krylov projection methods for model reduction , Ph.D. thesis, Department of Electrical Engineering, University of Illinois at Urbana–Champaign .
   Google Scholar
• Deutsch , E. 1975 . On matrix norms and logarithmic norms . Numer. Math. 24 , : 49 – 51 .
   Google Scholar
• Ström , T. 1975 . On logarithmic norms . SIAM J. Numer. Anal , 12 : 741 – 753 .
   Web of Science ®Google Scholar
• Higueras , I. and Garcia-Celayeta , B. 1999 . Logarithmic norms for matrix pencils . SIAM J. Matrix Anal. Appl , 20 : 646 – 666 .
   Web of Science ®Google Scholar
• Benner , P. , Ortí , E.S.Q. and Ortí , G.Q. 2000 . Balanced truncation model reduction of large scale dense systems on parallel computers . Math. Comput. Model. Dyn. Syst , 6 : 383 – 405 .
   Web of Science ®Google Scholar
• Penzl , T. 2000 . A cyclic low-rank smith method for large sparse lyapunov equations . SIAM J. Sci. Comp , 21 : 1401 – 1418 .
   Web of Science ®Google Scholar
• Gugercin , S. , Sorensen , D.C. and Antoulas , A.C. 2003 . A modified low-rank smith method for large-scale Lyapunov equations . Numer. Algorithm , 32 : 27 – 55 .
   Web of Science ®Google Scholar
• Li , J. and White , J. 2004 . Low-rank solution of Lyapunov equations . SIAM Rev , 46 : 693 – 713 .
   Web of Science ®Google Scholar
• Osborne , E.E. 1960 . On pre-conditioning of matrices . J. Assoc. Comput. Mach. 7 , : 338 – 345 .
   Google Scholar
• Chen , T. 2001 . Preconditioning sparse matrices for computing eigenvalues and solving linear systems equations , Berkeley : Ph.D. thesis, University of California .
   Google Scholar
• van der Schaft , A.J. 2000 . -Gain and Passivity Techniques in Nonlinear Control , London : Springer-Verlag .
   Google Scholar
• Wolf , T. , Lohmann , B. , Eid , R. and Kotyczka , P. 2010 . Passivity and structure preserving order reduction of linear port-Hamiltonian systems using Krylov subspaces . Eur. J. Control , 16 : 401 – 406 .
   Web of Science ®Google Scholar
• Salimbahrami , B. 2005 . Structure preserving order reduction of large scale second order models , Ph.D. thesis, Institute of Automatic Control, Technische Universität München .
   Google Scholar
• STMicroelectronics VNH2SP30-E Motor Driver Datasheet (2004), Available at http://www.st.com/stonline/products/literature/ds/10832/vnh2sp30-e.pdf (Accessed 20 July 2009) (http://www.st.com/stonline/products/literature/ds/10832/vnh2sp30-e.pdf (Accessed 20 July 2009))
   Google Scholar
• Panzer , H. , Hubele , J. , Eid , R. and Lohmann , B. 2009 . Generating a parametric finite element model of a 3D cantilever timoshenko beam using matlab , Tech. Rep. on Automatic Control, Lehrstuhl für Regelungstechnik, Technische Universität München .
   Google Scholar