Controllability and observability of linear delay systems : an algebraic approach
ESAIM: Control, Optimisation and Calculus of Variations (1998)
- Volume: 3, page 301-314
- ISSN: 1292-8119
Access Full Article
topHow to cite
topFliess, M., and Mounier, H.. "Controllability and observability of linear delay systems : an algebraic approach." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 301-314. <http://eudml.org/doc/90525>.
@article{Fliess1998,
author = {Fliess, M., Mounier, H.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {module theory; controllability; observability; delay systems},
language = {eng},
pages = {301-314},
publisher = {EDP Sciences},
title = {Controllability and observability of linear delay systems : an algebraic approach},
url = {http://eudml.org/doc/90525},
volume = {3},
year = {1998},
}
TY - JOUR
AU - Fliess, M.
AU - Mounier, H.
TI - Controllability and observability of linear delay systems : an algebraic approach
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 301
EP - 314
LA - eng
KW - module theory; controllability; observability; delay systems
UR - http://eudml.org/doc/90525
ER -
References
top- [1] Z. Bartosiewicz: Approximate controllability of neutral systems with delays in control, J. Diff. Eq., 51, 1984, 295-325. Zbl0487.93010MR735203
- [2] A. Bensoussan, G. Da Prato, M.C. Delfour, S.K. Mitter: Representation and Control of Infinite Dimensional Systems, 1, 2, Birkhäuser, Boston, 1992-1993. Zbl0790.93016MR2273323
- [3] K.P.M. Bhat, H.N. Koivo: Modal characterizations of controllability and observability for time-delay systems, IEEE Trans. Automat. Contr., 21, 1976, 292-293. Zbl0325.93005MR424297
- [4] H. Bourlès, M. Fliess: Finite poles and zeros of linear systems: an intrinsic approach, Internat J. Control, 68, 1997, 897-922. Zbl1034.93009MR1689711
- [5] J.W. Brewer, J.W. Bunce, F.S. Van Vleck: Linear Systems over Commutative Rings, Marcel Dekker, New York, 1986. Zbl0607.13001MR839186
- [6] D.A. Buchsbaum, D. Eisenbud: What makes a complex exact?J. Alg., 25, 1973, 259-268. Zbl0264.13007MR314819
- [7] C.I. Byrnes: On the control of certain deterministic, infinite-dimensional systems by algebro-geometric techniques, Amer. J. Math., 100, 1978, 1333-1381. Zbl0406.93017MR522703
- [8] R.M. Cohn: A difference-differential basis theorem, Canad. J. Math., 22, 1970, 1224-1237. Zbl0206.05104MR274428
- [9] D. Eisenbud: Commutative Algebra with a View toward Algebraic Geometry, Springer-Verlag, New York, 1995. Zbl0819.13001MR1322960
- [10] M. Fliess: Some basic structural properties of generalized linear systems, Systems Control Lett., 15, 1990, 391-396. Zbl0727.93024MR1084580
- [11] M. Fliess: A remark on Willems' trajectory characterization of linear controllability, Systems Control Lett., 19, 1992, 43-45. Zbl0765.93003MR1170986
- [12] M. Fliess: Reversible linear and non linear discrete time dynamics, IEEE Trans. Automat. Contr., 37, 1992, 1144-1153. Zbl0764.93058MR1178584
- [13] M. Fliess: Une interprétation algébrique de la transformation de Laplace et des matrices de transfert, Linear Alg. Appl., 203-204, 1994, 429-442. Zbl0802.93010MR1275520
- [14] M. Fliess, H. Bourlès: Discussing some examples of linear systems interconnections, Systems Control Lett., 27, 1996, 1-7. Zbl0877.93064MR1375906
- [15] M. Fliess, R. Hotzel: Sur les systèmes linéaires à dérivation non entière, C.R. Acad. Sci. Paris II, 324, 1997, 99-105. Zbl0870.93024
- [16] M. Fliess, H. Mounier: Quelques propriétés structurelles des systèmes linéaires à retards constants, C. R. Acad. Sci. Paris I, 319, 1994, 289-294. Zbl0805.93001MR1288420
- [17] M. Fliess, H. Mounier: Interpretation and comparison of various types of delay system controllabilities, In Proc. IFAC Conference System, Structure and Control, Nantes, 1995, 330-335.
- [18] E. Fornasini, M.E. Valcher: A polynomial matrix approach to the behavioral analysis of nd systems, In 3rd European Control Conference Proc., Rome, 1995, 1757-1762.
- [19] H. Glüsing-Lüerβen: A behavioral approach to delay differential systems, SIAM J. Contr. Opt., 35, 1997, 480-499. Zbl0876.93022MR1436634
- [20] A. Grothendieck, J.A. Dieudonné: Eléments de géométrie algébrique I, Springer-Verlag, Berlin1971. Zbl0203.23301
- [21] R. Hartshorne: Algebraic Geometry, Springer-Verlag, NewYork, 1977. Zbl0367.14001MR463157
- [22] R.E. Kalman, P.L. Falb, M.A. Arbib: Topics in Mathematical Systems Theory, McGraw-Hill, New York, 1969. Zbl0231.49001MR255260
- [23] E.W. Kamen: On an algebraic theory of systems defined by convolution operators, Math. Syst. Theory, 9, 1975, 57-74. Zbl0318.93003MR395953
- [24] E.W. Kamen: An operator theory of linear functional differential equations, J. Diff. Eq., 27, 1978, 274-297. Zbl0365.34080MR480283
- [25] E.W. Kamen, P.P. Khargonekar, A. Tannenbaum: Proper stable Bezout factorization and feedback control of linear time-delay systems, Internat. J. Control, 43, 1986, 837-857. Zbl0599.93047MR828360
- [26] T.Y. Lam: Serre's Conjecture, Springer-Verlag, Berlin, 1978. Zbl0373.13004MR485842
- [27] S. Lang: Algebra, 3rd ed., Addison-Wesley, Reading, MA, 1993. Zbl0848.13001MR197234
- [28] E.B. Lee, S. Neftci, A. Olbrot: Canonical forms for time delay systems, IEEE Trans. Automat. Contr., 27, 1982, 128-132. Zbl0469.93027MR673080
- [29] E.B. Lee, A. Olbrot: Observability and related structural results for linear hereditary systems, Internat. I. Control, 34, 1981, 1061-1078. Zbl0531.93015MR643872
- [30] A. Manitius, R. Triggiani: Function space controllability of retarded systems: a derivation from abstract operator conditions, SIAM J. Contr. Opt., 16, 1978, 599-645. Zbl0442.93009MR482505
- [31] A.S. Morse: Ring models for delay-differential systems, Automatica, 12, 1976, 529-531. Zbl0345.93023MR437162
- [32] H. Mounier: Propriétés structurelles des systèmes linéaires à retards : aspects théoriques et pratiques, Thèse, Université Paris-Sud, Orsay, 1995.
- [33] H. Mounier: Algebraic interpretations of the spectral controllability of a linear delay system, Forum Math., 10, 1998, 39-58. Zbl0891.93014MR1490137
- [34] H. Mounier: Stabilization of a class of linear delay systems, Math. Comp. Sim., 45, 1998, 329-338. Zbl1017.93514MR1622411
- [35] H. Mounier, J. Rudolph, M. Fliess, P. Rouchon: Tracking control of a vibrating string with an interior mass viewed as a delay system, ESAIM: Control Optimisation and Calculus of Variations, http://www.emath.fr/cocv/, 3, 1998, 315-321. Zbl0906.73046MR1644431
- [36] H. Mounier, P. Rouchon, J. Rudolph: Some examples of linear delay systems, RAIRO-JESA-APII, 31, 1997, 911-925.
- [37] H. Mounier, P. Rouchon, J. Rudolph: π-freeness of a long electric line, Comput. Eng. in Syst. Appl. IMACS Multiconference, Lille, 1996, 28-29.
- [38] D.A. O'Connor, T.J. Tarn: On the function space controllability of linear neutral systems, SIAM J. Contr. Opt., 21, 1983, 306-329. Zbl0509.93014MR690229
- [39] P. Picard, J.F. Lafay: Further results on controllability of linear systems with delays, In European Control Conference Proc., Rome, 1995, 3313-3318.
- [40] D. Quillen: Projective modules over polynomial rings, Inv. Math., 36, 1976, 167-171. Zbl0337.13011MR427303
- [41] P. Rocha, J. Willems: Behavioral controllability of D-D systems, SIAM J. Contr. Opt., 35, 1997, 254-264. Zbl0872.93013MR1430293
- [42] J. Rotman: An Introduction to Homological Algebra, Academic Press, New-York, 1979. Zbl0441.18018MR538169
- [43] L.H. Rowen: Ring Theory, Academic Press, Boston, 1991. Zbl0743.16001MR1095047
- [44] J.P. Serre: Faisceaux algébriques cohérents, Annals of Math., 61, 1955, 197-278. Zbl0067.16201MR68874
- [45] E.D. Sontag: Linear systems over commutative rings: a survey, Richerche di Automatica, 7, 1976, 1-34. Zbl0522.93020
- [46] M.W. Spong, T.J. Tarn: On the spectral controllability of delay-differential equations, IEEE Trans. Automat. Contr., 26, 1981, 527-528. Zbl0474.93014MR613571
- [47] A.A. Suslin: Projective modules over a polynomial ring are free (in Russian), Dokl. Akad. Nauk. S.S.S.R., 229, 1976, 1063-1066; English translation: Soviet Math. Dokl., 17, 1160-1164. Zbl0354.13010MR469905
- [48] Y. Yamamoto: Reachability of a class of infinite-dimensional linear systems: an external approach with applications to general neutral systems, SIAM J. Contr. Opt., 27, 1989, 217-234. Zbl0671.93003MR980231
- [49] D.C. Youla, G. Gnavi: Notes on n-dimensional system theory, IEEE Trans. Circuits Syst., 26, 1979, 105-111. Zbl0394.93004MR521657
- [50] D.C. Youla, P.F. Pickel: The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices, IEEE Trans. Circuits Syst., 31, 1984, 513-518. Zbl0553.13003MR747050
Citations in EuDML Documents
top- H. Mounier, J. Rudolph, M. Fliess, P. Rouchon, Tracking control of a vibrating string with an interior mass viewed as delay system
- Michel Fliess, Richard Marquez, Emmanuel Delaleau, Hebertt Sira-Ramírez, Correcteurs proportionnels-intégraux généralisés
- Luis Alejandro Márquez-Martínez, Claude H. Moog, Martín Velasco-Villa, Observability and observers for nonlinear systems with time delays
- Frédéric Rotella, Francisco Javier Carillo, Mounir Ayadi, Polynomial controller design based on flatness
- Ülle Kotta, Palle Kotta, Miroslav Halás, Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra
- Michel Fliess, Richard Marquez, Emmanuel Delaleau, Hebertt Sira–Ramírez, Correcteurs proportionnels-intégraux généralisés
- Frank Woittennek, Joachim Rudolph, Motion planning for a class of boundary controlled linear hyperbolic PDE’s involving finite distributed delays
- Frank Woittennek, Joachim Rudolph, Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays
- Michel Fliess, On the structure of linear recurrent error-control codes
- Michel Fliess, On the structure of linear recurrent error-control codes
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.