Abstract
This article is motivated by recent efforts concerned with finding continuous feedback laws u = α(x) that asymptotically stabilize control systems of the form ẋ = f(x, u) on R n. In particular we try to link ideas from nonlinear generalizations of the classical zero-dynamics techniques (compare e.g. [3, 10]), and results on asymptotic feedback stabilization of homogeneous systems (compare e.g. [1, 6, 7]).
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This work was partially supported by NSF grants DMS 88-05815 and DMS 90-07547 and an Arizona State University FGIA grant
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References
A. Andreini, A. Bacciotti, and G. Stefani, Global slabilizabibilly of homogeneous vector fields of odd degree, Systems and Control Letters 10 (1986) 251–256.
A. Bressan, Local asymptotic approximation of non-linear control systems, Int. J. Control 41 no.5 (1985) pp. 1331–1336.
C. I. Byrnes and A. Isidori, The analysis and design of nonlinear feedback systems, to appear in: IEEE Transactions Aut. Control.
R. Goodman, Nilpotent Lie Groups; Lecture Notes Mathematics vol.562 (1976) Berlin (Springer).
H. G. Hermes, Nilpotent approximations of control systems and distributions. SIAM J. Control & Opt. 24 no.4 (1986) pp. 731–736.
M. Kawski, Stabilization of nonlinear systems in the plane, Systems and Control Letters 12 (1989) pp. 169–175.
M. Kawski, Homogeneous stabilizing feedback laws, Control Theory and Advanced Technology (CTAT), 6 no.4 (1990).
L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976) pp.247–320.
G. Stefani, On the local controllability of a scalar-input control system, Proc. 24th IEEE Conf. Decision and Cntrl., Ft. Lauderdale, Florida, (1985).
H. J. Sussmann and P. Kokotovich, Peaking and Stabilization, Proc. 28th IEEE Conf. Decision and Cntrl., Tampa, Florida (1989) pp.1379–1391.
H. J. Sussmann, A general theorem on local controllability, SIAM J. Control & Opt. 25 no. l (1987) pp. 158–194.
F. W. Wilson, The structure of the level surfaces of a Lyapunov function, J. Diff. Equations 3 (1967) pp.323–329.
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© 1991 Birkhäuser Boston
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Kawski, M. (1991). Families of Dilations and Asymptotic Stability. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_25
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_25
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