Bibliography
Major publications by the team in recent years
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1J.-P. Barbot, D. Boutat, T. Floquet.
An observation algorithm for nonlinear systems with unknown inputs, in: Automatica, 2009, vol. 45, no 8, pp. 1970-1974.
http://hal.inria.fr/inria-00391819 -
2L. Belkoura, J.-P. Richard, M. Fliess.
Parameters estimation of systems with delayed and structured entries, in: Automatica, 2009, vol. 45, no 5, pp. 1117-1125.
http://hal.inria.fr/inria-00343801 -
3M. Fliess, C. Join.
A mathematical proof of the existence of trends in financial time series, in: International Conference on Systems Theory: Modelling, Analysis and Control, Maroc, Fes, A. E. Jai, L. Afifi, E. Zerrik (editors), Presses Universitaires de Perpignan, 2009, pp. 43-62, Plenary talk.
http://hal.inria.fr/inria-00352834 -
4M. Fliess.
Analyse non standard du bruit, in: Comptes-Rendus de l'Académie des Sciences, Série 1, Mathématiques, 2006, vol. 342, pp. 797-802.
http://hal.inria.fr/inria-00001134 -
5M. Fliess, M. Mboup, H. Mounier, H. Sira-Ramirez.
Questioning some paradigms of signal processing via concrete examples, in: Algebraic Methods in Flatness, Signal Processing and State Estimation, H. Sira-Ramirez, G. Silva-Navarro (editors), Editorial Lagares, 2003, pp. 1-21.
http://hal.inria.fr/inria-00001059 -
6M. Mboup, C. Join, M. Fliess.
Numerical differentiation with annihilators in noisy environment, in: Numerical Algorithms, 2009, vol. 50, no 4, pp. 439-467.
http://hal.inria.fr/inria-00319240 -
7W. Perruquetti, T. Floquet, E. Moulay.
Finite time observers: application to secure communication, in: IEEE Transactions on Automatic Control, 2008, vol. 53, no 1, pp. 356-360.
http://hal.inria.fr/inria-00176758 -
8S. Riachy, Y. Orlov, T. Floquet, R. Santiesteban, J.-P. Richard.
Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum, in: International Journal of Robust and Nonlinear Control, 2008, vol. 18, pp. 529-543.
http://hal.inria.fr/inria-00179854 -
9J.-P. Richard, T. Divoux.
Systèmes commandés en réseau, Hermès-Lavoisier, 2007, 234 p.
http://hal.inria.fr/inria-00179831 -
10G. Zheng, D. Boutat, J.-P. Barbot.
Single Output Dependent Observability Normal Form, in: SIAM Journal on Control and Optimization, 2007, vol. 46, no 6, pp. 2242-2255.
http://hal.inria.fr/inria-00179184
Articles in International Peer-Reviewed Journals
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11V. Azhmyakov, A. Polyakov, A. Poznyak.
Consistent approximations and variational description of some classes of sliding mode control processes, in: Journal of The Franklin Institute, January 2013. [ DOI : 10.1016/j.jfranklin.2013.01.011 ]
http://hal.inria.fr/hal-00922390 -
12F. J. Bejarano, T. Floquet, W. Perruquetti, G. Zheng.
Observability and Detectability of Singular Linear Systems with Unknown Inputs, in: Automatica, 2013, vol. 49, no 2.
http://hal.inria.fr/hal-00753706 -
13E. Bernuau, W. Perruquetti, E. Moulay.
Retraction obstruction to time-varying stabilization, in: Automatica, 2013, vol. 49, no 6, pp. 1941-1943.
http://hal.inria.fr/hal-00862934 -
14E. Bernuau, A. Polyakov, D. Efimov, W. Perruquetti.
Verification of ISS, iISS and IOSS properties applying weighted homogeneity, in: Systems & Control Letters, December 2013, vol. 62, no 12, pp. 1159-1167.
http://hal.inria.fr/hal-00877148 -
15J. Cieslak, D. Efimov, D. Henry.
Transient management of a supervisory fault-tolerant control scheme based on dwell-time conditions, in: International Journal of Adaptive Control and Signal Processing, January 2014. [ DOI : 10.1002/acs.2465 ]
http://hal.inria.fr/hal-00924618 -
16R. Delpoux, M. Bodson, T. Floquet.
Parameter estimation of permanent magnet stepper motors without mechanical sensors, in: Control Engineering Practice, January 2014.
http://hal.inria.fr/hal-00933297 -
17R. Delpoux, T. Floquet.
On-line parameter estimation via algebraic method: An experimental illustration, in: Asian Journal of Control, January 2014.
http://hal.inria.fr/hal-00933292 -
18N. Djeghali, M. Ghanes, S. Djennoune, J.-P. Barbot.
Sensorless Fault Tolerant Control for Induction Motors, in: International Journal of Control, Automation, and Systems, July 2013, vol. 11, no 3, pp. 563-576.
http://hal.inria.fr/hal-00923749 -
19D. Efimov, J. Cieslak, A. Zolghadri, D. Henry.
Actuator fault detection in aircraft systems: Oscillatory Failure Case study, in: Annual Reviews in Control, 2013, vol. 37, no 1, pp. 180 - 190. [ DOI : 10.1016/j.arcontrol.2013.04.007 ]
http://hal.inria.fr/hal-00801660 -
20D. Efimov, A. Fradkov, T. Iwasaki.
Exciting multi-DOF systems by feedback resonance, in: Automatica, May 2013, vol. 49, no 6, pp. 1782–1789.
http://hal.inria.fr/hal-00813506 -
21D. Efimov, W. Perruquetti, T. Raissi, A. Zolghadri.
Interval Observers for Time-Varying Discrete-Time Systems, in: IEEE Transactions on Automatic Control, December 2013.
http://hal.inria.fr/hal-00820937 -
22D. Efimov, W. Perruquetti, J.-P. Richard.
Interval estimation for uncertain systems with time-varying delays, in: International Journal of Control, May 2013.
http://hal.inria.fr/hal-00813314 -
23D. Efimov, W. Perruquetti, A. Shiriaev.
On existence of oscillations in hybrid systems, in: Nonlinear Analysis: Hybrid Systems, June 2014.
http://hal.inria.fr/hal-00906088 -
24D. Efimov, T. Raissi, S. Chebotarev, A. Zolghadri.
Interval State Observer for Nonlinear Time Varying Systems, in: Automatica, February 2013, vol. 49, no 1, pp. 200–205. [ DOI : 10.1016/j.automatica.2012.07.004 ]
http://hal.inria.fr/hal-00719911 -
25D. Efimov, T. Raissi, A. Zolghadri.
Control of nonlinear and LPV systems: interval observer-based framework, in: IEEE Transactions on Automatic Control, 2013.
http://hal.inria.fr/hal-00664106 -
26D. Efimov, T. Raissi, A. Zolghadri.
Set Adaptive Observers for LPV Systems: Application to Fault Detection, in: ASME Journal of Dynamic Systems, Measurement and Control, December 2013.
http://hal.inria.fr/hal-00843639 -
27M. Fliess, C. Join.
Model-free control, in: International Journal of Control, December 2013, vol. 86, no 12, pp. 2228-2252. [ DOI : 10.1080/00207179.2013.810345 ]
http://hal.inria.fr/hal-00828135 -
28M. Ghanes, J. Deleon, J.-P. Barbot.
Observer design for nonlinear systems under unknown time-varying delays, in: IEEE Transactions on Automatic Control, June 2013.
http://hal.inria.fr/hal-00749682 -
29M. Ghanes, M. Trabelsi, X. Lin-Shi, J.-P. Barbot, J.-M. Rétif, K. Busawon.
High gain observer for a three-cell chopper: Design and experimental results, in: International Journal of Robust and Nonlinear Control, September 2013. [ DOI : 10.1002/rnc.3063 ]
http://hal.inria.fr/hal-00923689 -
30O. Gibaru, L. Gajny, É. Nyiri.
L1C1 polynomial spline approximation algorithms for large data sets, in: Numerical Algorithms, November 2013. [ DOI : 10.1007/s11075-014-9828-x ]
http://hal.inria.fr/hal-00927555 -
31F. Hamerlain, T. Floquet, W. Perruquetti.
Experimental Tests of a Sliding Mode Controller for Trajectory Tracking of a Car-like Mobile Robot, in: Robotica, 2014, vol. 32, no 1, pp. 63-76.
http://hal.inria.fr/hal-00924745 -
32M. Hiliaret, M. Ghanes, O. Béthoux, J.-P. Barbot, D. Normand-Cyrot.
A Passivity-Based Controller for coordination of converters in a Fuel Cell System, in: Control Engineering Practice, August 2013, vol. 21, no 8, pp. 1097-1109. [ DOI : 10.1109/TVT.2013.2246202 ]
http://hal.inria.fr/hal-00923716 -
33T. Menard, E. Moulay, W. Perruquetti.
Homogeneous Approximations and Local Observer Design, in: ESAIM - Control Optimisation and Calculus of Variations, July 2013, vol. 19, no 03, pp. 906-929.
http://hal.inria.fr/hal-00787926 -
34A. Polyakov, D. Efimov, W. Perruquetti, J.-P. Richard.
Output Stabilization of Time-Varying Input Delay Systems Using Interval Observation Technique, in: Automatica, December 2013.
http://hal.inria.fr/hal-00847565 -
35S. Rahme, Y. Labit, F. Gouaisbaut, T. Floquet.
Sliding Modes for Anomaly Observation in TCP Networks: From Theory to Practice, in: IEEE Transactions on Control Systems Technology, May 2013, vol. 21, no 3, pp. 1031-1038. [ DOI : 10.1109/TCST.2012.2198648 ]
http://hal.inria.fr/hal-00734325 -
36S. Riachy, M. Ghanes.
A nonlinear controller for pneumatic servo systems: Design and experimental tests, in: IEEE Transactions on Mechatronics, September 2013. [ DOI : 10.1109/TMECH.2013.2280956 ]
http://hal.inria.fr/hal-00867054 -
37R. Seydou, T. Raissi, A. Zolghadri, D. Efimov.
Actuator fault diagnosis for flat systems: A constraint satisfaction approach, in: International Journal of Applied Mathematics & Computer Science, January 2013, vol. Vol 23, no N° 1.
http://hal.inria.fr/hal-00694775 -
38R. Tami, D. Boutat, G. Zheng.
Extended output depending normal form, in: Automatica, April 2013, vol. 7, pp. 2192-2198. [ DOI : 10.1016/j.automatica.2013.03.025 ]
http://hal.inria.fr/hal-00817332 -
39G. Zheng, J.-P. Barbot, D. Boutat.
Identification of the delay parameter for nonlinear time-delay systems with unknown inputs, in: Automatica, March 2013, vol. 6, pp. 1755-1760. [ DOI : 10.1016/j.automatica.2013.02.020 ]
http://hal.inria.fr/hal-00817331
Articles in Non Peer-Reviewed Journals
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40C. Join, G. Robert, M. Fliess.
Une "commande sans modèle" pour aménagements hydroélectriques en cascade, in: FlashX - La revue scientifique de l'Ecole polytechnique, July 2013, vol. 15, pp. 33-38.
http://hal.inria.fr/hal-00843678
Invited Conferences
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41L. Amet, M. Ghanes, J.-P. Barbot.
Sensorless control of a DC series motor, in: IFAC ALCOSP, Caen, France, July 2013.
http://hal.inria.fr/hal-00923720 -
42J.-P. Barbot.
An epistemology of observation theory and its application in the design of software sensor in power electronics., in: The 5th International Conference on Electronics Engineering (ICEE 2013), Oran, Algeria, Alipacha Adda, November 2013.
http://hal.inria.fr/hal-00908432 -
43D.-Y. Liu, T.-M. Laleg-Kirati, O. Gibaru, W. Perruquetti.
Fractional Order Numerical Differentiation with B-Spline Functions, in: The International Conference on Fractional Signals and Systems 2013, Ghent, Belgium, October 2013.
http://hal.inria.fr/hal-00859455
International Conferences with Proceedings
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44E. Bernuau, D. Efimov, W. Perruquetti, A. Polyakov.
On an extension of homogeneity notion for differential inclusions, in: European Control Conference 2013, Zurich, Switzerland, July 2013.
http://hal.inria.fr/hal-00801818 -
45E. Bernuau, A. Polyakov, D. Efimov, W. Perruquetti.
On ISS and iISS properties of homogeneous systems, in: European Control Conference 2013, Zurich, Switzerland, July 2013.
http://hal.inria.fr/hal-00801817 -
46E. Bernuau, A. Polyakov, D. Efimov, W. Perruquetti.
Robustness of finite-time stability property for sliding modes, in: Joint SSSC, TDS, FDA 2013, Grenoble, France, February 2013.
http://hal.inria.fr/hal-00745673 -
47D. Boutat, J.-P. Barbot, M. Darouach.
A New Algorithm to Compute Inverse Dynamic of a Class of Nonlinear Systems, in: 52nd IEEE Conference on Decision and Control, Florence, Italy, December 2013.
http://hal.inria.fr/hal-00923663 -
48E. Brousseau, B. Arnal, S. Thiery, É. Nyiri, O. Gibaru, J. Mayor.
Towards CNC Automation in AFM Probe-Based Nano Machining, in: 8th International Conference on MicroManufacturing (ICOMM 2013), Canada, University of Wisconsin-Madison, March 2013, pp. 499-506.
http://hal.inria.fr/hal-00880967 -
49S. Chebotarev, D. Efimov, T. Raissi, A. Zolghadri.
On Interval Observer Design for a Class of Continuous-Time LPV Systems, in: IFAC Nolcos 2013, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00844390 -
50J. Cieslak, D. Efimov, A. Zolghadri, D. Henry, P. Goupil.
Oscillatory Failure Case Detection for Aircraft using Non-Homogeneous Differentiator in Noisy Environment, in: 2nd CEAS Specialist Conference on Guidance, Navigation & Control, Delft, Netherlands, co-sponsored by IEEE and AIAA, April 2013.
http://hal.inria.fr/hal-00787966 -
51O. Datcu, R. Tauleigne, J.-P. Barbot.
A new algorithm for the analysis of strange attractors, in: International Symposium on Signals, Circuits and Systems (ISSCS), Iasi, Romania, July 2013.
http://hal.inria.fr/hal-00923697 -
52O. Datcu, R. Tauleigne, A. Vlad, J.-P. Barbot.
Observability-singularity manifolds in the context of chaos based cryptography, in: International Conference on systems and Control (ICSC'13), Alger, Algeria, October 2013.
http://hal.inria.fr/hal-00923700 -
53J. De Miras, C. Join, M. Fliess, S. Riachy, S. Bonnet.
Active magnetic bearing: A new step for model-free control, in: 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, IEEE, December 2013, CD p.
http://hal.inria.fr/hal-00857649 -
54R. Delpoux, H. Sira-Ramirez, T. Floquet.
Acceleration Feedback via an algebraic state estimation method, in: 52th IEEE Conference on Decision and Control,, Florence, Italy, December 2013.
http://hal.inria.fr/hal-00881164 -
55D. Efimov, W. Perruquetti, T. Raissi, A. Zolghadri.
On Interval Observer Design for Time-Invariant Discrete-Time Systems, in: European Control Conference 2013, Zurich, Switzerland, July 2013.
http://hal.inria.fr/hal-00801806 -
56D. Efimov, W. Perruquetti, J.-P. Richard.
On reduced-order interval observers for time-delay systems, in: European Control Conference 2013, Zurich, Switzerland, July 2013.
http://hal.inria.fr/hal-00801809 -
57D. Efimov, W. Perruquetti, A. Shiriaev.
Conditions of existence of oscillations for hybrid systems, in: IFAC Nolcos 2013, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00844408 -
58L. Etienne, S. Digennaro, J.-P. Barbot.
Active Ground Vehicle Control with use of a Super-Twisting Algorithm in the Presence of Parameter Variations, in: 3d International Conference on Systems and Control (ICSC13), Alger, Algeria, October 2013.
http://hal.inria.fr/hal-00923757 -
59C. Fiter, L. Hetel, W. Perruquetti, J.-P. Richard.
A Robust Polytopic Approach for State-Dependent Sampling, in: 12th biannual European Control Conference, Zurich, Switzerland, July 2013.
http://hal.inria.fr/hal-00849833 -
60C. Fiter, L. Hetel, W. Perruquetti, J.-P. Richard.
A Self-Triggered Control Based on Convex Embeddings for Perturbed LTI Systems, in: 9th IFAC Symposium on Nonlinear Control Systems, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00849840 -
61M. Fliess, C. Join.
Systematic and multifactor risk models revisited, in: First Paris Financial Management Conference, Paris, France, December 2013.
http://hal.inria.fr/hal-00920175, http://khuongnguyen.free.fr/PFMC-2013/Program_Papers.pdf -
62C. Join, F. Chaxel, M. Fliess.
"Intelligent" controllers on cheap and small programmable devices, in: 2nd International Conference on Control and Fault-Tolerant Systems, SysTol'13, Nice, France, October 2013, CDROM p.
http://hal.inria.fr/hal-00845795 -
63Y. Khaled, J.-P. Barbot, K. Busawon, D. Benmerzouk.
Impulsive observer-based control for linear systems using irregularly sampled measurements, in: IEEE AFRICON 2013, Mauritius, Mauritius, September 2013.
http://hal.inria.fr/hal-00923640 -
64Y. Khaled, J.-P. Barbot, D. Benmerzouk, K. Busawon.
High order sliding mode: is it useful in the design of observer under sparse measurement?, in: IFAC Joint 2013 SSSC, TDS, FDA, Grenoble, France, February 2013.
http://hal.inria.fr/hal-00923765 -
65Y. Khaled, J.-P. Barbot, K. Busawon, D. Benmerzouk.
From restricted isometry property to observability under sparse measurement, in: International Conference on Systems and Control, Alger, Algeria, October 2013.
http://hal.inria.fr/hal-00923629 -
66S. Kolyubin, D. Efimov, V. Nikiforov, A. Bobtsov.
Control of Nonlinear Systems Using Multiple Model Black-Box Identification, in: IFAC Nolcos 2013, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00844410 -
67D.-Y. Liu, T.-M. Laleg-Kirati, O. Gibaru.
Fractional order differentiation by integration: an application to fractional linear systems, in: 6th IFAC Workshop on Fractional Differentiation and its Applications, Grenoble, France, February 2013.
http://hal.inria.fr/hal-00759819 -
68D.-Y. Liu, T.-M. Laleg-Kirati, O. Gibaru, W. Perruquetti.
Identification of fractional order systems using modulating functions method, in: 2013 American Control Conference, 2013, Washington, DC, United States, June 2013.
http://hal.inria.fr/hal-00801425 -
69Y. Ma, G. Zheng, W. Perruquetti.
Cooperative path planning for mobile robots based on visibility graph, in: IEEE 32nd Chinese Control Conference, Xi'an, China, IEEE, July 2013.
http://hal.inria.fr/hal-00910186 -
70Y. Ma, G. Zheng, W. Perruquetti.
Real-time Identification of different types of non-holonomic mobile robots, in: 9th IFAC Symposium on Nonlinear Control Systems, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00910210 -
71Y. Ma, G. Zheng, W. Perruquetti.
Real-time local path planning for mobile robots, in: IEEE 9th International Workshop on Robot Motion and Control, Wasowo, Poland, IEEE, July 2013.
http://hal.inria.fr/hal-00910182 -
72Y. Ma, G. Zheng, W. Perruquetti, Z. Qiu.
Control of nonholonomic wheeled mobile robots via -PID controller, in: IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan, IEEE, November 2013.
http://hal.inria.fr/hal-00910218 -
73H. Omran, L. Hetel, J.-P. Richard, F. Lamnabhi-Lagarrigue.
On the stability of input-affine nonlinear systems with sampled-data control, in: ECC'2013, Zurich, Switzerland, July 2013, NC p.
http://hal.inria.fr/hal-00830881 -
74S. Parsegov, A. Polyakov, P. Shcherbakov.
Fixed-time consensus algorithm for multi-agent systems with integrator dynamics, in: 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems, Koblenz, Germany, IFAC, September 2013, pp. 110-115. [ DOI : 10.3182/20130925-2-DE-4044.00055 ]
http://hal.inria.fr/hal-00920078 -
75A. Polyakov, D. Efimov, W. Perruquetti.
Finite-time Stabilization Using Implicit Lyapunov Function Technique, in: IFAC Nolcos 2013, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00844386 -
76A. Polyakov, D. Efimov, W. Perruquetti, J.-P. Richard.
Interval Observer Approach to Output Stabilization of Time-Varying Input Delay System, in: European Control Conference 2013, Zurich, Switzerland, July 2013.
http://hal.inria.fr/hal-00801821 -
77A. Polyakov, A. Poznyak, J.-P. Richard.
Robust Output Stabilization of Time-Varying Input Delay Systems using Attractive Ellipsoid Method, in: IEEE Conference on Decision and Control, Florence, Italy, IEEE, December 2013, pp. 934-939.
http://hal.inria.fr/hal-00920047 -
78A. Si Ammour, S. Djennoune, M. Ghanes, J.-P. Barbot, M. Bettayeb.
Sliding mode control for uncertain input delay fractional order systems, in: IFAC Joint 2013 SSSC, TDS, FDA, Grenoble, France, February 2013.
http://hal.inria.fr/hal-00923777 -
79R. Tami, D. Boutat, G. Zheng.
Nonlinear observer normal form with output injection and extended dynamic, in: 9th IFAC Symposium on Nonlinear Control Systems, Toulouse, Ethiopia, IFAC, September 2013.
http://hal.inria.fr/hal-00910212 -
80R. Tami, G. Zheng, D. Boutat, D. Aubry.
Partial observability normal form for nonlinear functional observers design, in: IEEE 32nd Chinese Control Conference, Xi'an, China, IEEE, July 2013.
http://hal.inria.fr/hal-00910190 -
81R. Ushirobira, W. Perruquetti, M. Mboup, M. Fliess.
Algebraic parameter estimation of a multi-sinusoidal waveform signal from noisy data, in: European Control Conference, Zurich, Switzerland, April 2013.
http://hal.inria.fr/hal-00819048 -
82G. Zheng, D. Efimov, W. Perruquetti.
Interval state estimation for uncertain nonlinear systems, in: IFAC Nolcos 2013, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00844397
National Conferences with Proceedings
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83L. Laval, J.-P. Barbot, C. Letellier.
Sur la synchronisation de systèmes chaotiques bidirectionnellement couplés, in: Rencontre du Non-Linéaire 2013, Paris, France, March 2013.
http://hal.inria.fr/hal-00923671
Conferences without Proceedings
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84L. Gajny, É. Nyiri, O. Gibaru.
Approximation spline L1C1 par fenêtres glissantes pour le signal et l'image, in: Journées du Groupe de Travail en Modélisation Géométrique 2013, Marseille, France, March 2013.
http://hal.inria.fr/hal-00841326 -
85L. Hetel, E. Fridman, T. Floquet.
Sampled-data control of LTI systems with relays: a convex optimization approach, in: 9th IFAC Symposium on Nonlinear Control Systems, Toulouse, France, September 2013.
http://hal.inria.fr/hal-00923825
Scientific Books (or Scientific Book chapters)
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86A. Zolghadri, D. Henry, J. Cieslak, D. Efimov, P. Goupil.
Fault Diagnosis and Fault-Tolerant Control and Guidance for Aerospace Vehicles From theory to flight tests, Advances in Industrial Control, Springer London Ltd, September 2013, 216 p.
http://hal.inria.fr/hal-00869253
Patents
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87P. Goupil, R. Dayre, A. Gheorghe, D. Efimov, J. Cieslak, A. Zolghadri.
Procédé et dispositif de détection d'une anomalie sur un aéronef, 2013, no FR20130055665.
http://hal.inria.fr/hal-00869250
Other Publications
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88D.-Y. Liu, O. Gibaru, W. Perruquetti, T.-M. Laleg-Kirati.
Fractional order differentiation by integration and error analysis in noisy environment: Part 1 continuous case, January 2013.
http://hal.inria.fr/hal-00779176 -
89D.-Y. Liu, O. Gibaru, W. Perruquetti, T.-M. Laleg-Kirati.
Fractional order differentiation by integration and error analysis in noisy environment: Part 2 discrete case, January 2013.
http://hal.inria.fr/hal-00779182