A study of behaviors

Linear Algebra and Its Applications

Volumn 351-352, Issue , 2002, Pages 303-380

  Fuhrmann, P A ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Behavior homomorphism; Behaviors; Linear systems; Polynomial models; Rational models; Strict system equivalence

Indexed keywords

CONTROLLABILITY; LINEAR SYSTEMS; MATRIX ALGEBRA; POLYNOMIALS;

BEHAVIOR HOMOMORPHISM; BEHAVIORS; POLYNOMIAL MODELS; RATIONAL MODELS; SYSTEM EQUIVALENCE;

EQUIVALENCE CLASSES;

EID: 5444250620     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(02)00282-3     Document Type: Article

References (51)

1. A.C. Antoulas, PhD thesis, ETH Zürich, 1980
2. G. Basile, and G. Marro Controlled and conditioned invariant subspaces in linear system theory J. Optim. Theory Appl. 3 1973 306 316
3. M. Bisiacco, M.E. Valcher, Behavior decompositions and two sided diophantine equations, Automatica, 2001
4. H. Blomberg, and R. Ylinen Algebraic Theory for Multivariable Linear Systems 1983 Academic Press London
5. F.M. Callier, and C. Desoer Multivariable Feedback Systems 1982 Springer New York
6. S. Eilenberg Automata, Languages and Machines 1974 Academic Press New York
7. E. Emre, and M.L.J. Hautus A polynomial characterization of (A, B)-invariant and reachability subspaces SIAM J. Control Optim. 18 1980 420 436
8. V. Fonf, Private communication, 2000
9. P.A. Fuhrmann Algebraic system theory: an analyst's point of view J. Franklin Inst. 301 1976 521 540
10. P.A. Fuhrmann On strict system equivalence and similarity Int. J. Control 25 1977 5 10
11. P.A. Fuhrmann Duality in polynomial models with some applications to geometric control theory IEEE Trans. Automat. Control AC-26 1981 284 295
12. P.A. Fuhrmann Linear Systems and Operators in Hilbert Space 1981 McGraw-Hill New York
13. P.A. Fuhrmann A duality theory for robust control and model reduction Linear Algebra Appl. 203-204 1994 471 578
14. P.A. Fuhrmann, and R. Ober On Coprime Factorizations, T. Ando volume 1993 Birkhauser Basel
15. P.A. Fuhrmann, and J.C. Willems Factorization indices at infinity for rational matrix functions Integral Equations Operator Theory 2 1979 287 301
16. P.A. Fuhrmann, and J.C. Willems A study of (A,B)-invariant subspaces via polynomial models Int. J. Control 31 1980 467 494
17. M.L.J. Hautus, P.A. Fuhrmann, On the zero module of rational matrix functions, in: Proceedings CDC Conferemce, Albuquerque, 1980
18. M.L.J. Hautus, and M. Heymann Feedback - an algebraic approach SIAM J. Control 16 1978 83 105
19. M. Heymann Controllability subspaces and feedback simulation SIAM J. Control Optim. 14 1976 769 789
20. P.J. Hilton, and Y. Wu A Course in Modern Algebra 1974 Wiley-Interscience New York
21. D. Hinrichsen, and D. Prätzel-Wolters Module theoretic characterization of system equivalence in time domain in: Algebraic and Geometric Methods in Linear System Theory AMS Lectures in Applied Mathematics vol. 18 1980 137 156
22. D. Hinrichsen, and D. Prätzel-Wolters Solution modules and system equivalence Int. J. Control 32 1980 777 802
23. D. Hinrichsen, and D. Prätzel-Wolters Generalized Hermite matrices and complete invariants of strict system equivalence SIAM J. Control Optim. 21 1983 289 305
24. M. Hou, A.C. Pugh, and G.E. Hayton Generalized transfer functions and input/output equivalence Int. J. Control 68 1997 1163 1178
25. T. Kailath Linear Systems 1980 Prentice-Hall Englewood Cliffs, NJ
26. R.E. Kalman, P. Falb, and M. Arbib Topics in Mathematical System Theory 1969 McGraw-Hill New York
27. P.P. Khargonekar, and E. Emre Further results on polynomial characterizations of (F,G)-invariant and reachability subspaces IEEE Trans. Automat. Control AC-27 1982 352 366
28. M. Kuijper, First order representations of linear systems, Ph.D. thesis, Catholic University of Brabant, 1992
29. M. Kuijper First Order Representations of Linear Systems 1994 Birkhauser Basel
30. M. Kuijper, and J.M. Schumacher Realization of autoregressive equations in pencil and descriptor form SIAM J. Control Optim. 28 1990 1162 1189
31. U. Oberst Multidimensional constant linear systems Acta Appl. Math. 20 1990 1 175
32. A.B. Özgüler Polynomial characterizations of (H,F)-invariant subspaces with applications Linear Algebra Appl. 73 1986 1 31
33. A.B. Özgüler Linear Multichannel Control 1994 Prentice-Hall Englewood Cliffs, NJ
34. L. Pernebo Notes on strict system equivalence Int J. Control 25 1977 21 38
35. J.W. Polderman, and J.C. Willems Introduction to Mathematical System Theory 1997 Springer New York
36. D. Prätzel-Wolters, Feedback morphism between linear systems - a unified approach to state space systems, transfer functions and system matrices, Ph.D. dissertation, University of Bremen, 1981
37. H.H. Rosenbrock State-Space and Multivariable Theory 1970 John Wiley New York
38. J. Rosenthal, and J.M. Schumacher Realization by inspection IEEE Trans. Automat. Control AC-42 1997 1257 1263
39. J. Rosenthal, Connections between linear systems and convolutional coding theory, preprint, 2000
40. J.M. Schumacher Transformations of linear systems under external equivalence Linear Algebra Appl. 102 1988 1 34
41. J.M. Schumacher Linear system representations H. Nijmeijer, J.M.S. Schumacher, Three Decades of Mathematical System Theory. A Collection of Surveys at the Occasioon of the Fiftieth Birthday of Jan C. Willems Lecture Notes in Control and Information Sciences vol. 135 1989 Springer Berlin 382 408
42. M.E. Valcher, A behavioral approach to classic polynomial matrix descriptions, Systems and Control Lett. 40 (2000) 279-288
43. S. Weiland, and A. Stoorvogel Rational representation of behaviors: interconnectability and stabilizability Math. Control Signals Systems 10 1997 125 164
44. J.C. Willems From time series to linear systems. Part I: Finite-dimensional linear time invariant systems Automatica 22 1986 561 580
45. J.C. Willems Models for dynamics U. Kirchgraber, H.O. Walther, Dynamics Reported vol. 2 1989 Wiley-Teubner 171 269
46. J.C. Willems Paradigms and puzzles in the theory of dynamical systems IEEE Trans. Automat. Control AC-36 1991 259 294
47. H. Wimmer A Jordan factorization theorem for polynomial matrices Proc. Amer. Math. Soc. 75 1979 201 206
48. W.M. Wonham Linear Multivariable Control second ed. 1979 Springer New York
49. B.F. Wyman, and M.K. Sain The zero module and essential inverse systems IEEE Trans. Circuits and Systems 28 1981 112 126
50. B.F. Wyman, M.K. Sain, G. Conte, and A. Perdon On the zeros and poles of a transfer function Linear Algebra Appl. 122-124 1989 123 144
51. E. Zerz, On strict system equivalence for multidimensional systems, Int. J. Control, 2000