Patchy vector fields and asymptotic stabilization
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 445-471. 
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     author = {Ancona, Fabio and Bressan, Alberto},
     title = {Patchy vector fields and asymptotic stabilization},
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     pages = {445--471},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1693900},
     zbl = {0924.34058},
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     url = {http://archive.numdam.org/item/COCV_1999__4__445_0/}
}
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Ancona, Fabio; Bressan, Alberto. Patchy vector fields and asymptotic stabilization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 445-471. http://archive.numdam.org/item/COCV_1999__4__445_0/

[1] Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. 7 ( 1983) 1163-1173. | MR | Zbl

[2] A. Bacciotti Local stabilizability of nonlinear control systems. Series on advances in mathematics for applied sciences 8, World Scientific, Singapore ( 1992). | MR | Zbl

[3] R.W. Brockett, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, R.W. Brockett, R.S. Millman and H.J. Sussmann, Eds., Birkhauser, Boston ( 1983) 181-191. | MR | Zbl

[4] F.H. Clarke, Yu.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization . IEEE Trans. Automat. Control 42 ( 1997 ) 1394-1407. | MR | Zbl

[5] F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R.J. Stern, Feedback stabilization and Lyapunov functions , to appear. | MR | Zbl

[6] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Qualitative properties of trajectories of control systems: A survey . J. Dynamic Control Systems 1 ( 1995) 1-47. | MR | Zbl

[7] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth analysis and control theory 178, Springer-Verlag, New York ( 1998). | MR | Zbl

[8] G. Colombo, On extremal solutions of differential inclusions. Bull. Polish. Acad. Sci. 40 ( 1992) 97-109. | MR | Zbl

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

[10] J.-M. Coron and L. Rosier, A relation between continuous time-varying and discontinuous feedback stabilization. J. Math. Systems, Estimation, and Control 4 ( 1994) 67-84. | MR | Zbl

[11] J.-M. Coron, Global asymptotic stabilization for controllable systems without drift . Math. of Control, Signals, and Systems 5 ( 1992) 295-312. | MR | Zbl

[12] J.-M. Coron, Stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws . SIAM J. Control Optim. 33 ( 1995) 804-833. | MR | Zbl

[13] J.-M. Coron, L. Praly and A. Teel, Feedback stabilization of nonlinear systems: sufficient conditions and Lyapunov and input-output techniques, in Trends in Control: A European Perspective, A. Isidori, Eds., Springer, London ( 1995) 293-348. | MR

[14] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Sides, Kluwer Acad. Publ. ( 1988). | Zbl

[15] O. Hájek, Discontinuos differential equations, I-II. J. Differential Equations 32 ( 1979) 149-185. | MR | Zbl

[16] H. Hermes, Discontinuous vector fields and feedback control, in Differential Equations and Dynamical Systems, J.K. Hale and J.P. La Salle, Eds., Academic Press, New York, ( 1967) 155-165. | MR | Zbl

[17] H. Hermes, On the synthesis of stabilizing feedback controls via Lie algebraic methods. SIAM J. Control Optim. 10 ( 1980) 352-361. | MR | Zbl

[18] N.N. Krasovskii and A.I. Subbotin, Positional differential games, Nauka, Moscow, ( 1974) [in Russian]. Revised English translation: Game-theoretical control problems, Springer-Verlag, New York ( 1988). | MR | Zbl

[19] Yu.S. Ledyaev and E.D. Sontag, A remark on robust stabilization of general asymptotically controllable systems, in Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD ( 1997) 246-251.

[20] Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. J. Nonlinear Anal, to appear. | MR | Zbl

[21] S. Nikitin, Piecewise-constant stabilization. SIAM J. Control Optim. to appear. | MR | Zbl

[22] E.P. Ryan, On Brockett's condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. SIAM J. Control Optim. 32 ( 1994) 1597-1604. | MR | Zbl

[23] E.D. Sontag and H.J. Sussmann, Remarks on continuous feedback, in Proc. IEEE Conf. Decision and Control, Aulbuquerque, IEEE Publications, Piscataway ( 1980) 916-921.

[24] E.D. Sontag Nonlinear regulation: The piecewise linear approach . IEEE Trans. Automat. Control 26 ( 1981) 346-358. | MR | Zbl

[25] E.D. Sontag, Feedback stabilization of nonlinear systems, in Robust Control of Linear Systems and Nonlinear Control, M.A. Kaashoek, J.H. van Shuppen and A.C.M. Ran, Eds., Birkhäuser, Cambridge, MA ( 1990) 61-81. | MR | Zbl

[26] E.D. Sontag, Mathematical control theory, deterministic finite dimensional systems, Springer-Verlag, New York ( 1990). | MR | Zbl

[27] E.D. Sontag, Stability and stabilization: Discontinuities and the effect of disturbances, in Proc. NATO Advanced Study Institute - Nonlinear Analysis, Differential Equations, and Control (Montreal, Jul/Aug 1998), F.H. Clarke and R.J. Stern, Eds., Kluwer ( 1999) 551-598. | MR | Zbl

[28] H.J. Sussmann, Subanalytic sets and feedback control . J. Differential Equations 31 ( 1979) 31-52. | MR | Zbl