A framework for the solution of the generalized realization problem

Linear Algebra and Its Applications

Volumn 425, Issue 2-3, 2007, Pages 634-662

  Mayo, A J ^a   Antoulas, A C ^a  

^a Rice University   (United States)

Author keywords

Bi tangential interpolation; Descriptor systems; Generalized controllability matrices; Generalized observability matrices; Hankel matrices; Loewner matrices; Rational interpolation; Realization; Shifted Loewner matrices; Tangential interpolation

Indexed keywords

BI-TANGENTIAL INTERPOLATION; DESCRIPTOR SYSTEMS; GENERALIZED CONTROLLABILITY MATRICES; GENERALIZED OBSERVABILITY MATRICES; HANKEL MATRICES; LOEWNER MATRICES; RATIONAL INTERPOLATION; REALIZATION; SHIFTED LOEWNER MATRICES; TANGENTIAL INTERPOLATION;

COMPUTATIONAL METHODS; DATA REDUCTION; INTERPOLATION; MATRIX ALGEBRA; NUMERICAL METHODS;

PROBLEM SOLVING;

EID: 34447535436     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2007.03.008     Document Type: Article

References (22)

1. Antoulas A.C. Approximation of large-scale dynamical systems. Advances in Design and Control vol. DC-06 (2005), SIAM, Philadelphia
2. Anderson B.D.O., and Antoulas A.C. Rational interpolation and state variable realizations. Linear Algebra and its Applications 137/138 (1990) 479-509
3. Antoulas A.C., and Anderson B.D.O. On the scalar rational interpolation problem. IMA J. Math. Control Inform. 3 (1986) 61-68
4. Antoulas A.C., and Anderson B.D.O. State space and polynomial approaches to rational interpolation. Progr. Systems Control Theory, Proceedings MTNS-89 3 (1989) 73-82
5. Antoulas A.C., Ball J.A., Kang J., and Willems J.C. On the solution of the minimal rational interpolation problem. Linear Algebra Appl. 137/138 (1990) 511-573
6. Ball J., Gohberg I., and Rodman L. Interpolation of Rational Matrix Functions. Operator Theory: Advances and Applications vol. 45 (1990), Birkhäuser
7. Belevitch V. Interpolation Matrices. Philips Res. Repts. (1970) 337-369
8. Benner P., and Sokolov V.I. Partial realization of descriptor systems. Syst. Control Lett. 55 11 (2006) 929-938
9. Dai L. Singular control systems. Lecture Notes in Control and Information Sciences vol. 118 (1989), Springer-Verlag, Berlin
10. Fiedler M. Hankel and Loewner matrices. Linear Algebra Appl. 58 (1984) 75-95
11. Gallivan K., Vandendorpe A., and Van Dooren P. Model reduction of MIMO systems via tangential interpolation. SIAM J. Matrix Anal. Appl. 26 (2004) 328-349
12. 2 model reduction, submitted for publication.
13. Kuijper M., and Schumacher J.M. Realization of autoregressive equations in pencil and descriptor form. SIAM J. Control Optimiz. SICON-58 (1990) 1162-1189
14. A.J. Mayo, Interpolation from a realization point of view, Ph.D. dissertation, Department of Electrical and Computer Engineering, Rice University, 2007.
15. A.J. Mayo, A.C. Antoulas, New results on interpolation and model reduction, in: Proc. 17th Intl. Symposium on Math. Theory of Networks and Systems, MTNS06, Kyoto, 2006, pp. 1643-1651.
16. Nevanlinna R. Über Beschränkte analytische Funktionen. Ann. Acad. Sci. Fenn. A 32 7 (1929)
17. Pick G. Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt sind. Math. Ann. 77 (1916) 7-23
18. Rosenbrock H.H. Structural properties of linear dynamical systems. Int. J. Control 20 (1974) 191-202
19. Stykel T. Gramian based model reduction for descriptor systems. Math. Control Signals Syst. MCSS-16 (2004) 297-319
20. Verghese G.C., Levy B.C., and Kailath T. A generalized state-space for singular systems. IEEE Trans. Aut. Contr. AC-26 (1981) 811-831
21. Youla D.C., and Saito M. Interpolation with positive real functions. J. Franklin Inst. 284 (1967) 77-108
22. Delsarte Ph., Genin Y., and Kamp Y. On the role of the Nevanlinna-Pick problem in circuits and system theory. Circuit Theory Appl. 9 (1981) 177-187