Smooth homogeneous asymptotically stabilizing feedback controls
ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997), pp. 13-32. 
@article{COCV_1997__2__13_0,
     author = {Hermes, Henry},
     title = {Smooth homogeneous asymptotically stabilizing feedback controls},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {13--32},
     publisher = {EDP-Sciences},
     volume = {2},
     year = {1997},
     mrnumber = {1440077},
     zbl = {0872.93072},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_1997__2__13_0/}
}
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Hermes, Henry. Smooth homogeneous asymptotically stabilizing feedback controls. ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997), pp. 13-32. http://archive.numdam.org/item/COCV_1997__2__13_0/

[1] F. Ancona: Decomposition of homogeneous vector fields of degree one and representation of the flow, Annales de l'Institut Henri Poincaré, J. Nonlinear Analysis (to appear). | EuDML | Numdam | MR | Zbl

[2] M. Bardi: A boundary value problem for the minimum time function, SIAM J. Control and Opt., 27, 1989, 776-785. | MR | Zbl

[3] R. Bianchini and G. Stephani: Graded Approximations and Controllability along a trajectory, SIAM J. Control and Opt., 28, 1990, 903-924. | MR | Zbl

[4] R.W. Brockett: Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, 27, R. Brockett, R.S. Millman, H.J. Sussmann, eds., Birkhäuser, Boston, 181-191, 1983. | MR | Zbl

[5] J.-M. Coron: A necessary condition for feedback stabilization, Systems and Control Lett., 14, 1990, 227-232. | MR | Zbl

[6] J.-M. Coron: On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws, SIAM J. Control and Opt., 33, 1995, 804-833. | MR | Zbl

[7] W. Dayawansa, C. Martin and G. Knowles: Asymptotic stabilization of a class of smooth two dimensional systems, SIAM J. Control and Opt., 28, 1990, 1321-1349. | MR | Zbl

[8] W. Dayawansa and C. Martin: Asymptotic stabilization of low dimensional systems, in Systems and Control Theory, C.I. Byrnes and A. Kurzhansky, eds., Birkhäuser, Boston, 53-67, 1991. | MR | Zbl

[9] L.C. Evans and M.R. James: The Hamilton-Jacobi-Bellman equation for time optimal control, SIAM J. Control and Opt., 27, 1989, 1477-1489. | MR | Zbl

[10] H. Hermes: Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, in Diff. Eqs., Stability and Control, S. Elaydi, ed., Lecture Notes in Pure and Applied Math., 127, Marcel Dekker Inc., 249-260, 1991. | MR | Zbl

[11] H. Hermes: Large time local controllability via homogeneous approximation, SIAM J. Control and Opt., 34, 1996, 1291-1299. | MR | Zbl

[12] H. Hermes: Nilpotent and high-order approximations of vector field systems, SIAM Review, 33, 1991, 238-264. | MR | Zbl

[13] H. Hermes: Asymptotically stabilizing feedback controls and the nonlinear regulator problem, SIAM J. Control and Opt., 29, 1991, 185-196. | MR | Zbl

[14] H. Hermes: Asymptotically stabilizing feedback controls, J. Diff. Eqs., 92, 1991, 76-89. | MR | Zbl

[15] M. Kawski: Geometric homogeneity and stabilization, in NOLCOS'95, 1, 164-169, 1995.

[16] J.B. Pomet: Explicit design of time varying stabilizing control laws for a class of controllable systems without drift, Systems et Control Letters, 18, 1992, 147-158. | MR | Zbl

[17] E.B. Lee and L. Markus: Foundations of Optimal Control Theory, John Wiley, N.Y., 1967. | MR | Zbl

[18] L.P. Rothschild and E.M. Stein: Hypoelliptic differential operators and nilpotent groups, Acta Math., 137, 1976, 247-320. | MR | Zbl

[19] L. Rosier: Homogeneous Liapunov function for continuous vector field, System and Control Lett., 19, 1992, 467-473. | MR | Zbl

[20] R. Sepulchre: Contributions to nonlinear control systems analysis by means of the direct method of Liapunov, Ph.D thesis, Universite Catholique de Louvain, 1994.

[21] G. Stefani: Local properties of nonlinear control systems, in Geometric Theory of Nonlinear Control Systems, B. Jakubczyk, W. Respondek, K. Tchon, eds., Tech. Univ., Wroclaw, 219-226, 1984. | MR | Zbl

[22] H.J. Sussmann: A general theorem on local controllability, SIAM J. Control and Opt., 25, 1987, 158-194. | MR | Zbl

[23] J. Tsinias: Triangular systems: A global extension of Coron-Praly theorem on the existence of feedback-integrator stabilizers, (preprint) 1996. | Zbl