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Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems. (English) Zbl 0959.93046
The paper concerns the feedback stabilization of a class of affine control processes using Lyapunov functions.

93D15 Stabilization of systems by feedback
93D30 Lyapunov and storage functions
93C10 Nonlinear systems in control theory
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[1] D. Aeyels, Stabilization of a class of nonlinear systems by smooth feedback control. Systems Control Lett. 5 ( 1985) 289-294. Zbl0569.93056 MR791542 · Zbl 0569.93056 · doi:10.1016/0167-6911(85)90024-6
[2] Z. Artstein, Stabilization with relaxed control. Nonlinear Anal. TMA 7 ( 1983) 1163-1173. Zbl0525.93053 MR721403 · Zbl 0525.93053 · doi:10.1016/0362-546X(83)90049-4
[3] A. Bacciotti, Local stabilizability of nonlinear control systems. World Scientifîc, Singapore, River Edge, London, Ser. Adv. Math. Appl. Sci. 8 ( 1992). Zbl0757.93061 MR1148363 · Zbl 0757.93061
[4] R.W. Brockett, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, edited by R.W. Brockett, R.S. Millman and H.J. Sussmann. Basel-Boston, Birkäuser ( 1983) 181-191. Zbl0528.93051 MR708502 · Zbl 0528.93051
[5] R.T. Bupp, D.S. Bernstein and V.T. Coppola, A benchmark problem for nonlinear control design. Internat J. Robust Nonlinear Control 8 ( 1998) 307-310. MR1611573
[6] R.T. Bupp, D.S. Bernstein and V.T. Coppola, Experimental implementation of integrator back-stepping and passive nonlinear controllers on the RTAC testbed. Internat J. Robust Nonlinear Control 8 ( 1998) 435-457. Zbl0925.93352 MR1611580 · Zbl 0925.93352 · doi:10.1002/(SICI)1099-1239(19980415/30)8:4/5<435::AID-RNC355>3.0.CO;2-4
[7] J.-M. Coron, L. Praly and A.R. Teel, Feedback stabilization of nonlinear system: Sufficient conditions and lyapunov and input-output techniques, in Trends in Control, a European Perspective, edited by A. Isidori. Springer-Verlag ( 1995) 283-348. MR1448452
[8] L. Faubourg, La déformation de fonctions de Lyapunov, Rapport de DEA d’automatique et informatique industrielle. INRIA-Université de Lille 1 ( 1997).
[9] L. Faubourg and J.-B. Pomet, Strict control Lyapunov functions for homogeneous Jurdjevic-Quinn type systems, in Nonlinear Control Systems Design Symposium (NOLCOS’98), edited by H. Huijberts, H. Nijmeijer, A. van der Schaft and J. Scherpen. IFAC ( 1998) 823-829.
[10] L. Faubourg and J.-B. Pomet, Design of control Lyapunov functions for ”Jurdjevic-Quinn” systems, in Stability and Stabilization of Nonlinear Systems, edited by D. Aeyels et al. Springer-Verlag, Lecture Notes in Contr. & Inform. Sci. ( 1999) 137-150. Zbl0945.93607 MR1714587 · Zbl 0945.93607 · link.springer.de
[11] J.-P. Gauthier, Structure des Systèmes non-linéaires. Éditions du CNRS, Paris ( 1984). Zbl0606.58001 MR767635 · Zbl 0606.58001
[12] W. Hahn, Stability of Motion. Springer-Verlag, Berlin, New-York, Grundlehren Math. Wiss. 138 ( 1967). Zbl0189.38503 MR223668 · Zbl 0189.38503
[13] V. Jurdjevic and J.P. Quinn, Controllability and stability. J. Differential Equations 28 ( 1978) 381-389. Zbl0417.93012 MR494275 · Zbl 0417.93012 · doi:10.1016/0022-0396(78)90135-3
[14] M. Kawski, Homogeneous stabilizing feedback laws. Control Theory and Adv. Technol. 6 ( 1990), 497-516. MR1092775
[15] H.K. Khalil, Nonlinear Systems. MacMillan, New York, Toronto, Singapore ( 1992). Zbl0969.34001 MR1201326 · Zbl 0969.34001
[16] J. Kurzweil, On the inversion of Ljapunov’s second theorem on stability of motion. AMS Trans., Ser. II 24 ( 1956) 19-77. Zbl0127.30703 · Zbl 0127.30703 · eudml:11835
[17] J.-P. LaSalle, Stability theory for ordinary differential equations. J. Differential Equations 4 ( 1968) 57-65. Zbl0159.12002 MR222402 · Zbl 0159.12002 · doi:10.1016/0022-0396(68)90048-X
[18] W. Liu, Y. Chitour and E. Sontag, Remarks on finite gain stabilizability of linear systems subject to input saturation, in 32th IEEE Conf. on Decision and Control. San Antonio, USA ( 1993) 1808-1813.
[19] F. Mazenc, Stabilisation de trajectoires, ajout d’intégration, commandes saturées, Thèse de doctorat. École des Mines de Paris ( 1989).
[20] P. Morin, Robust stabilization of the angular velocity of a rigid body with two actuators. European J. Control 2 ( 1996) 51-56. Zbl0858.93057 · Zbl 0858.93057
[21] R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited. Systems Control Lett. 18 ( 1992) 93-98. Zbl0743.93082 MR1149353 · Zbl 0743.93082 · doi:10.1016/0167-6911(92)90013-I
[22] G. Sallet, Historique des techniques de Jurdjevic-Quinn(private communication).
[23] R. Sépulchre, M. Janković and P.V. Kokotović, Constructive Nonlinear Control. Springer-Verlag, Comm. Control Engrg. Ser. ( 1997). Zbl1067.93500 MR1481435 · Zbl 1067.93500
[24] E.D. Sontag, Feedback stabilization of nonlinear systems, in Robust control of linear systems and nonlinear control, Vol. 2 of proceedings of MTNS’89, edited by M.A. Kaashoek, J.H. van Schuppen and A. Ran. Basel-Boston, Birkhäuser ( 1990) 61-81. Zbl0735.93063 MR1115377 · Zbl 0735.93063
[25] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 1. Publish or Perish, Houston, second Ed. ( 1979). Zbl0439.53005 · Zbl 0439.53005
[26] J. Tsinias, Remarks on feedback stabilizability of homogeneous systems. Control Theory and Adv. Technol. 6 ( 1990) 533-542. MR1092777
[27] J. Zhao and I. Kanellakopoulos, Flexible back-stepping design for tracking and disturbance attenuation. Internat J. Robust Nonlinear Control 8 ( 1998) 331-348. Zbl0925.93824 MR1611575 · Zbl 0925.93824 · doi:10.1002/(SICI)1099-1239(19980415/30)8:4/5<331::AID-RNC358>3.0.CO;2-A
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