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Finite-time stabilization and stabilizability of a class of controllable systems. (English) Zbl 0994.93049
Summary: A finite-time control problem for a class of controllable systems is considered. Explicit formulae are proposed for the finite-time stabilization of a chain of power-integrators, and then discussions about a generalized class of nonlinear systems are given.

MSC:
93D15Stabilization of systems by feedback
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References:
[1] Athans, M.; Falb, P.: Optimal control: an introduction to theory and its applications. (1966) · Zbl 0196.46303
[2] Bacciotti, A.; Rosier, L.: Lyapunov functions and stability in control theory. Lecture note in control and information sciences 267 (2001) · Zbl 0968.93004
[3] S. Bhat, D. Bernstein, Finite time stability of homogeneous systems, Proceedings of ACC, Albuquerque, NM, 1997, pp. 2513--2514.
[4] Bhat, S.; Bernstein, D.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE trans. Automat. control 43, No. 5, 678-682 (1998) · Zbl 0925.93821
[5] Bhat, S.; Bernstein, D.: Finite-time stability of continuous autonomous systems. SIAM J. Control optim. 38, 751-766 (2000) · Zbl 0945.34039
[6] Celikovsky, S.; Aranda-Bricaire, E.: Constructive nonsmooth stabilization of triangular systems. Systems control lett. 32, No. 1, 79-91 (1999)
[7] Celikovsky, S.; Nijmeijer, H.: On the relation between local controllability and stabilizability for a class of nonlinear system. IEEE trans. Automat. control 42, No. 1, 90-94 (1997) · Zbl 0871.93042
[8] Coron, J.; Praly, L.: Adding an integrator for the stabilization problem. Systems control. Lett. 17, 89-107 (1991) · Zbl 0747.93072
[9] Haimo, V.: Finite time controllers. SIAM J. Control optim. 24, No. 4, 760-770 (1986) · Zbl 0603.93005
[10] J. Han, Nonlinear design methods for control systems, 14th World Congress of IFAC, Beijing, 1999, pp. F521--526.
[11] Hermes, H.: Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. Differential equations, stability and control, 249-260 (1991)
[12] Hong, Y.; Huang, J.; Xu, Y.: On an output feedback finite-time stabilization problem. IEEE trans. Automat. control 46, No. 2, 305-309 (2001) · Zbl 0992.93075
[13] Y. Hong, G. Yang, L. Bushnell, H. Wang, Global finite time stabilization: from state feedback to output feedback, Proceedings of IEEE CDC, Sydney, Australia, 2000.
[14] Kawski, M.: Stabilization of nonlinear systems in the plane. Systems control lett. 12, No. 2, 169-175 (1989) · Zbl 0666.93103
[15] Nijmeijer, H.; Van Der Schaft, A.: Nonlinear dynamic control systems. (1990) · Zbl 0701.93001
[16] L. Praly, Generalized weighted homogeneity and state dependent time scale for linear controllable systems, Proceedings of IEEE CDC, San Diego, 1997, pp. 4342--4347.
[17] Rosier, L.: Homogeneous Lyapunov function for homogeneous continuous vector field. Systems control lett. 19, No. 4, 467-473 (1992) · Zbl 0762.34032
[18] H. Wang, Y. Hong, L. Bushnell, Nonsmooth bifurcation control, Proceedings of ACC, Arlington, VA, 2001.