Patchy vector fields and asymptotic stabilization

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1. [1] Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. 7 ( 1983) 1163-1173. Zbl0525.93053MR721403
2. [2] A. BacciottiLocal stabilizability of nonlinear control systems. Series on advances in mathematics for applied sciences 8, World Scientific, Singapore ( 1992). Zbl0757.93061MR1148363
3. [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. Zbl0528.93051MR708502
4. [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. Zbl0892.93053MR1472857
5. [5] F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R.J. Stern, Feedback stabilization and Lyapunov functions , to appear. Zbl0961.93047MR1780907
6. [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. Zbl0951.49003MR1319056
7. [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). Zbl1047.49500MR1488695
8. [8] G. Colombo, On extremal solutions of differential inclusions. Bull. Polish. Acad. Sci. 40 ( 1992) 97-109. Zbl0771.34017MR1401862
9. [9] J.-M. Coron, A necessary condition for feedback stabilization . Systems Control Lett. 14 ( 1990) 227-232. Zbl0699.93075MR1049357
10. [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. Zbl0925.93827MR1298548
11. [11] J.-M. Coron, Global asymptotic stabilization for controllable systems without drift . Math. of Control, Signals, and Systems 5 ( 1992) 295-312. Zbl0760.93067MR1164379
12. [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. Zbl0828.93054MR1327239
13. [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. MR1448452
14. [14] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Sides, Kluwer Acad. Publ. ( 1988). Zbl0664.34001
15. [15] O. Hájek, Discontinuos differential equations, I-II. J. Differential Equations 32 ( 1979) 149-185. Zbl0365.34017MR534546
16. [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. Zbl0183.15905MR222424
17. [17] H. Hermes, On the synthesis of stabilizing feedback controls via Lie algebraic methods. SIAM J. Control Optim. 10 ( 1980) 352-361. Zbl0477.93046MR579546
18. [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). Zbl0298.90067MR437107
19. [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. [20] Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. J. Nonlinear Anal, to appear. Zbl0947.34054MR1695080
21. [21] S. Nikitin, Piecewise-constant stabilization. SIAM J. Control Optim. to appear. Zbl0922.93043MR1680818
22. [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. Zbl0806.93049MR1297100
23. [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. [24] E.D. SontagNonlinear regulation: The piecewise linear approach . IEEE Trans. Automat. Control 26 ( 1981) 346-358. Zbl0474.93039MR613541
25. [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. Zbl0735.93063MR1115377
26. [26] E.D. Sontag, Mathematical control theory, deterministic finite dimensional systems, Springer-Verlag, New York ( 1990). Zbl0703.93001MR1070569
27. [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. Zbl0937.93034MR1695014
28. [28] H.J. Sussmann, Subanalytic sets and feedback control . J. Differential Equations 31 ( 1979) 31-52. Zbl0407.93010MR524816

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