9 à IV.I2 correspondent aux réponses indicielles en boucle fermée. On peut constater que Ym! et Um! après de faibles oscillations, convergent assez rapidement ,
l Le système de la figure 1, où Gl (s) E lFtlIoo et G2(S) E lFtlIoo, est stable de manière interne si et seuiement si ,
O(s) et G-1 (s) dans H alors O(s) est outer IDIoo 00 ,
IO) i) d'inversion matricielle ,
Al -A2A4A3) et (Al + A2A4A3) ne sont pas singulières, on a les relations suivantes: (A.VII.II.a) (A. VII.II.b) ,
A) =1= 0, on obtient: det(F) =det(A) det(E -C A-l B) ,
Design of an Hoo controller Application to an induction motor, Msc Degree in Engineering Report, Imperial College of Science, ) et Ecole Supérieure d'Electricité, p.89, 1991. ,
Controller reduction: concepts and approaches, IEEE Transactions on Automatic Control, vol.34, issue.8, pp.802-81292, 1989. ,
DOI : 10.1109/9.29422
Controller design: moving from theory to practice, IEEE Control Systems, vol.13, issue.4, pp.16-25, 1992. ,
DOI : 10.1109/37.229554
Computer-controlled systems, 1990. ,
Multivariable frequency-weighted order reduction, Journal of Guidance, Control, and Dynamics, vol.39, issue.6, pp.97-107, 1989. ,
DOI : 10.1109/TAC.1982.1102945
A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control, IEEE Transactions on Automatic Control, vol.37, issue.4, pp.418-43570, 1992. ,
DOI : 10.1109/9.126576
Introduction to matrix analysis, 1970. ,
implantation d'une loi de commande: application à la plate-forme Eurostar, exposé à Matra Marconi Space, 1995. ,
URL : https://hal.archives-ouvertes.fr/tel-01748572
Frequency weighted closed-Ioop balanced reduction, 2nd European Control Conference, pp.697-70193, 1993. ,
Hoo controller reduction with closed-Ioop stability considerations, 32nd Conference on Decision and Control, pp.2923-292484, 1993. ,
On inner-outer and spectral factorizations, The 23rd IEEE Conference on Decision and Control, p.23 ,
DOI : 10.1109/CDC.1984.272438
Model reduction for control systems design, ph.D. Dissertations, Dep. Aeronaut. Astronaut, 1984. ,
Madel reduction with balanced realizations: an error bound and a frequency weighted generalization, 23rd Conference on Decision and Control, pp.127-132, 1984. ,
Lecture Notes in Control and Information SciencesA course in Hoocontrol theory, 1987. ,
Digital control of dynamic systems, 1990. ,
Hoo design for satellite attitude control, 1994. ,
Eléments de spécification du problème de paramétrisation du correcteur Eurostar, 1994. ,
Hoa controller order reduction technique based on normalized coprime factors for space control systems on board implementation, European Control Conference, p.94, 1995. ,
Inherent design limitations for linear sampled-data feedhack systems, American Control Conference, pp.3227-323193, 1994. ,
DOI : 10.1109/acc.1994.735169
Parametrizations in control, estimation and filtering problems, 1993. ,
-error bounds???, International Journal of Control, vol.127, issue.6, pp.1115-119389, 1984. ,
DOI : 10.1109/TIT.1961.1057636
Robust stabilization of normalized coprime factor plant description with Hoo-bounded uncertainty, IEEE Trans. Automat. Control, vol.34, issue.8, p.92, 1989. ,
A structured approximation problem with applications to frequency weighted model reduction, IEEE Transactions on Automatic Control, vol.37, issue.4, pp.447-46593, 1992. ,
DOI : 10.1109/9.126578
Controller reduction: weights for stability and performance preservation, Proceedings of 32nd IEEE Conference on Decision and Control, pp.2903-290894, 1993. ,
DOI : 10.1109/CDC.1993.325729
Performance-preserving frequency weighted controller approximation: a coprime factorisation approach, Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp.2720-272590, 1994. ,
DOI : 10.1109/CDC.1994.411391
Matrix computations, 1988. ,
On inner-outer factorization", systems & controlletters Il, pp.93-95 ,
Prentice hall information and system sciences series: "Linear robust control, Thomas Kailath, Series Editor, p.90, 1995. ,
Matrix analysisMinimum uncorrelated unit noise in state-space digital filtering, IEEE Trans. Acoust. Speech, Signal Processing, pp.25-273, 1977. ,
A new set of invariants for linear systems--Application to reduced order compensator design, IEEE Transactions on Automatic Control, vol.28, issue.10, pp.953-96491, 1983. ,
DOI : 10.1109/TAC.1983.1103159
H???-optimal controller discretization, International Journal of Robust and Nonlinear Control, vol.10, issue.2, pp.125-13792, 1991. ,
DOI : 10.1007/BFb0007371
A new approach to the discretization of continuous-time controllers, IEEE Transactions on Automatic Control, vol.37, issue.2, pp.214-223, 1992. ,
DOI : 10.1109/9.121622
Frequency-weighted optimal Hankel-norm approximation of stable transfer functions, Systems & Control Letters, vol.5, issue.4, pp.229-236, 1985. ,
DOI : 10.1016/0167-6911(85)90014-3
Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms, IEEE Transactions on Automatic Control, vol.32, issue.2, pp.115-122, 1987. ,
DOI : 10.1109/TAC.1987.1104549
Controller order reduction with guaranteed stability and performance, American Control Conference, pp.1697-1698, 1988. ,
Optimal FWL design of state-space digital systems with weighted sensitivity minimization and sparseness consideration, Fundamental theory and applications, pp.365-377, 1992. ,
DOI : 10.1109/81.139287
Controller reduction via stable factorization and balancing, International Journal of Control, vol.365, issue.2, pp.507-53190, 1986. ,
DOI : 10.1109/TAC.1984.1103497
Coprime factorization controller reduction with bezout identity induced frequency weighting, Automatica, vol.26, issue.2, pp.233-24990, 1990. ,
DOI : 10.1016/0005-1098(90)90118-2
Reduced-order controller design using coprime factor model reduction, IEEE Transactions on Automatic Control, vol.35, issue.3, pp.369-373, 1990. ,
DOI : 10.1109/9.50362
ModeI reduction via fractional representation ,
A fractional approach to model reductionBlock implementation of recursive digital filters. New structures and properties, American Control Conference IEEE Trans. Circuits and Syst, pp.1041-104725, 1978. ,
Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control, vol.26, issue.1, pp.17-3276, 1981. ,
DOI : 10.1109/TAC.1981.1102568
Synthesis of minimum roundoff noise fixed point digital filters, MUS-91, pp.551-562, 1976. ,
DOI : 10.1109/TCS.1976.1084254
Controller reduction by H/sub infinity /-balanced truncation, IEEE Transactions on Automatic Control, vol.36, issue.6, pp.668-68284, 1991. ,
DOI : 10.1109/9.86941
A connection between state-space and doubly coprime fractional representations, AC-29, pp.831-832, 1984. ,
DOI : 10.1109/TAC.1984.1103674
Discrete-time control systems ,
Model reduction via balanced state space representations, IEEE Transactions on Automatic Control, vol.27, issue.2, pp.382-38778, 1982. ,
DOI : 10.1109/TAC.1982.1102945
Discretizing continuous-data control systems, Computer-Aided Design, vol.10, issue.5, pp.299-30684, 1978. ,
DOI : 10.1016/0010-4485(78)90031-3
Digitalization of existing continuous control systems, IEEE Transactions on Automatic Control, vol.29, issue.3, 1984. ,
DOI : 10.1109/TAC.1984.1103507
Digital signal processing in the UK, Electronics and Power, vol.33, issue.3, 1987. ,
DOI : 10.1049/ep.1987.0120
A necessary and sufficient condition for quantization errors to be uniform and white, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.25, issue.5, pp.25-442, 1977. ,
DOI : 10.1109/TASSP.1977.1162977
Beyond singular values and loop shapes, Journal of Guidance, Control, and Dynamics, vol.14, issue.1 ,
DOI : 10.1049/ip-d.1982.0053
Optimal design of state - space digital filters by simultaneous minimization of sensitivity and roundoff noise, CAS-31, pp.884-888, 1984. ,
DOI : 10.1109/TCS.1984.1085426
On the sensitivity of linear state-space systems, CAS-33, pp.502-51083, 1986. ,
DOI : 10.1109/TCS.1986.1085951
On generalized balanced realizations, IEEE Trans ,
Control System SynthesisA Factorization Approach, 1985. ,
Normalised coprime factorizations for nonstrictly proper systems, IEEE Transactions on Automatic Control, vol.33, issue.3, pp.300-301 ,
DOI : 10.1109/9.408
Frequency weighted closed-Ioop order reduction in the control design configuration, 33rd Conference on Decision and Control, pp.2714-271995, 1994. ,
Frequency weighted closed-Ioop balanced controller reduction using normalized coprin1e factor descriptions, American Control Conference, p.93, 1995. ,
Frequency-weighted model reduction with Loo error bounds ,
DOI : 10.1016/0167-6911(93)90114-l