Previous |  Up |  Next

Article

Title: On a class of linear delay systems often arising in practice (English)
Author: Fliess, Michel
Author: Mounier, Hugues
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 37
Issue: 3
Year: 2001
Pages: [295]-308
Summary lang: English
.
Category: math
.
Summary: We study the tracking control of linear delay systems. It is based on an algebraic property named $\pi $-freeness, which extends Kalman’s finite dimensional linear controllability and bears some similarity with finite dimensional nonlinear flat systems. Several examples illustrate the practical relevance of the notion. (English)
Keyword: delay system
Keyword: $\pi $-freeness
Keyword: tracking control
Keyword: Kalman’s finite dimensional linear controllability
Keyword: finite dimensional nonlinear flat systems
MSC: 93A10
MSC: 93B05
MSC: 93B25
MSC: 93C05
MSC: 93C23
MSC: 93C25
idZBL: Zbl 1265.93061
idMR: MR1859087
.
Date available: 2009-09-24T19:39:39Z
Last updated: 2015-03-26
Stable URL: http://hdl.handle.net/10338.dmlcz/135410
.
Reference: [1] Artstein Z.: Linear systems with delayed control: a reduction.IEEE Trans. Automat. Control 27 (1982), 869–879 MR 0680488, 10.1109/TAC.1982.1103023
Reference: [2] Bensoussan A., Prato G. Da, Delfour M. C., Mitter S. K.: Representation and Control of Infinite Dimensional Systems, vol.1 & 2. Birkhäuser, Boston 1992 & 1993 MR 1182557
Reference: [3] Brethé D., Loiseau J. J.: A result that could bear fruit for the control of delay-differential systems.In: Proc. IEEE MSCA’96. Chania 1996
Reference: [4] Bhat K., Koivo H.: Modal characterizations of controllability and observability for time-delay systems.IEEE Trans. Automat. Control 21 (1976), 292–293 MR 0424297, 10.1109/TAC.1976.1101165
Reference: [5] Byrnes C. I., Spong, M., Tarn T. J.: A several complex variables approach to feedback stabilization of linear neutral delay-differential systems.Math. Systems Theory 17 (1984), 97–133 Zbl 0539.93064, MR 0739983, 10.1007/BF01744436
Reference: [6] Drakunov S., Özgüner U.: Generalized sliding modes for manifold control of distributed parameter systems.In: Variable Structure and Lyapounov Control (A. S. Zinober, ed., Lecture Notes in Control and Information Sciences 193), Springer, London 1994, pp. 109–129
Reference: [7] Fliess M.: Some basic structural properties of generalized linear systems.Systems Control Lett. 15 (1990), 391–396 Zbl 0727.93024, MR 1084580, 10.1016/0167-6911(90)90062-Y
Reference: [8] Fliess M.: A remark on Willems’ trajectory characterization of linear controllability.Systems Control Lett. 19 (1992), 43–45 Zbl 0765.93003, MR 1170986, 10.1016/0167-6911(92)90038-T
Reference: [9] Fliess M.: Une interprétation algébrique de la transformation de Laplace et des matrices de transfert.Linear Algebra Appl. 203–204 (1994), 429–442 Zbl 0802.93010, MR 1275520
Reference: [10] Fliess M.: Variations sur la notion de commandabilité.In: Quelques aspects de la théorie du contrôle. Proc. Journée annuelle Soc. Math. France, Paris 2000, pp. 47–86 MR 1799559
Reference: [11] Fliess M., Bourlès H.: Discussing some examples of linear system interconnections.System Control Lett. 27 (1996), 1–7 Zbl 0877.93064, MR 1375906, 10.1016/0167-6911(95)00029-1
Reference: [12] Fliess M., Lévine J., Martin, P., Rouchon P.: Flatness and defect of non-linear systems: introductory theory and applications.Internat. J. Control 61 (1995), 1327–1361 MR 1613557, 10.1080/00207179508921959
Reference: [13] Fliess M., Lévine J., Martin, P., Rouchon P.: A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems.IEEE Trans. Automat. Control 44 (1999), 922–937 Zbl 0964.93028, MR 1690537, 10.1109/9.763209
Reference: [15] Fliess M., Mounier H.: Quasi-finite linear delay systems: theory and applications.In: Proc. IFAC Workshop Linear Time Delay Systems, Grenoble 1998, pp. 211–215
Reference: [16] Fliess M., Marquez, R., Mounier H.: PID like regulators for a class of linear delay systems.In: Proc. European Control Conference, Porto 2001
Reference: [17] Fliess M., Marquez, R., Mounier H.: An extension of predictive control, PID regulators and Smith predictors to some linear delay systems.Internat. J. Control. Submitted Zbl 1021.93015, MR 1916231
Reference: [18] Kalman R. E., Falb, L., Arbib M. A.: Topics in Mathematical System Theory.McGraw–Hill, New York 1969 Zbl 0231.49002, MR 0255260
Reference: [19] Lam T. Y.: Serre’s Conjecture.Springer, Berlin 1978 Zbl 0373.13004, MR 0485842
Reference: [20] Lang S.: Algebra.Third edition. Addison–Wesley, Reading, MA 1993 Zbl 1063.00002
Reference: [21] Manitius A. J., Olbrot A. W.: Finite spectrum assignment problem for systems with delays.IEEE Trans. Automat. Control 24 (1979), 541–553 Zbl 0425.93029, MR 0538808, 10.1109/TAC.1979.1102124
Reference: [22] Marshall J., Górecki H., Korytowski, A., Walton K.: Time Delay Systems Stability and Performance Criteria with Applications.Ellis Horwood, New York 1992 Zbl 0769.93001
Reference: [23] Martin P., Murray R. M., Rouchon P.: Flat systems.In: Plenary Lectures and Mini–Courses, ECC 97 (G. Bastin and M. Gevers, eds.), Brussels 1997, pp. 211–264
Reference: [24] Morse A. S.: Ring models for delay-differential systems.Automatica 12 (1976), 529–531 Zbl 0345.93023, MR 0437162, 10.1016/0005-1098(76)90013-3
Reference: [25] Mounier H.: Propriétés structurelles des systèmes linéaires à retards: aspects théoriques et pratiques.Thèse, Université Paris-Sud, Orsay 1995
Reference: [26] Mounier H.: Algebraic interpretations of the spectral controllability of a linear delay system.Forum Mathematicum 10 (1998), 39–58 Zbl 0891.93014, MR 1490137, 10.1515/form.10.1.39
Reference: [27] Mounier H., Rouchon, P., Rudolph J.: Some examples of linear systems with delays.J. Europ. Syst. Autom. 31 (1997), 911–925
Reference: [28] Mounier H., Rudolph J.: Flatness based control of nonlinear delay systems: Example of a class of chemical reactors.Internat. J. Control 71 (1998), 838–871, special issue “Recent Advances in the Control of Non-linear Systems” MR 1658504, 10.1080/002071798221614
Reference: [30] Olbrot A. W.: Stabilizability, detectability, and spectrum assignment for linear autonomous systems with time delays.IEEE Trans. Automat. Control 23 (1978), 887–890 MR 0528786, 10.1109/TAC.1978.1101879
Reference: [31] Petit N., Creff, Y., Rouchon P.: Motion planning for two classes of nonlinear systems with delays depending on the control.In: Proc. 37th IEEE Conference on Decision and Control, 1998
Reference: [32] Quillen D.: Projective modules over polynomial rings.Invent. Math. 36 (1976), 167–171 Zbl 0337.13011, MR 0427303, 10.1007/BF01390008
Reference: [33] Rocha P., Willems J. C.: Behavioral controllability of D-D systems.SIAM J. Control Optim. 35 (1987), 254–264 MR 1430293, 10.1137/S0363012995283054
Reference: [34] Rotman J.: An Introduction to Homological Algebra.Academic Press, Orlando 1979 Zbl 1157.18001, MR 0538169
Reference: [35] Rowen L. H.: Ring Theory.Academic Press, Boston 1991 Zbl 0922.00017, MR 1095047
Reference: [36] Serre J.–P.: Faisceaux algébriques cohérents.Annals of Math. 61 (1955), 197–278 Zbl 0067.16201, MR 0068874
Reference: [37] Sontag E. D.: Linear systems over commutative rings: a survey.Richerche Automat. 7 (1976), 1–34
Reference: [38] Spong M. W., Tarn T. J.: On the spectral controllability of delay-differential equations.IEEE Trans. Automat. Control 26 (1981), 527–528 Zbl 0474.93014, MR 0613571, 10.1109/TAC.1981.1102654
Reference: [40] Willems J. C.: Paradigms and puzzles in the theory of dynamical systems.IEEE Trans. Automat. Control 36 (1991), 259–294 Zbl 0737.93004, MR 1092818, 10.1109/9.73561
Reference: [41] Youla D. C., Gnavi G.: Notes on $n$-dimensional system theory.IEEE Trans. Circuits and Systems 26 (1979), 105–111 Zbl 0394.93004, MR 0521657, 10.1109/TCS.1979.1084614
Reference: [42] Youla D. C., Pickel P. F.: The Quillen–Suslin theorem and the structure of n-dimensional elementary polynomial matrices.IEEE Trans. Circuits and Systems 31 (1984), 513–518 Zbl 0553.13003, MR 0747050, 10.1109/TCS.1984.1085545
Reference: [43] Zampieri S.: Modellizzazione di Sequenze di Dati Mutlidimensionali.Tesi, Università di Padova 1993
.

Files

Files Size Format View
Kybernetika_37-2001-3_7.pdf 1.661Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo