Abstract
This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abed, E.H., and J-H. Fu, “Local stabilization and bifurcation control, I. Hopf bifurcation,” Systems and Control Letters 7 (1986): 11–17.
Aeyels, D., “Stabilization of a class of nonlinear systems by a smooth feedback control,” Systems and Control Letters, 5 (1985): 289–294.
Artstein, Z., “Stabilization with relaxed controls,” Nonl. Anal., TMA 7 (1983): 1163–1173.
Baccioti, A., and P. Boieri, “Linear stabilizability of planar nonlinear systems,” to appear in Math. of Control, Signals, and Systems.
Boothby, W.M., and R. Marino, “Feedback stabilization of planar nonlinear systems,” Systems and Control Letters 12 (1989): 87–92.
Brockett, R.W., “Asymptotic stability and feedback stabilization,” in Differential Geometric Control theory ( R.W. Brockett, R.S. Millman, and H.J. Sussmann, eds.), Birkhauser, Boston, 1983, pp. 181–191.
Byrnes, C.I. and A. Isidori, “New results and counterexamples in nonlinear feedback stabilization,” Systems and Control Letters,12(1989), Number 5.
Dayawansa, W.P., and C.F. Martin, “Asymptotic stabilization of two dimensional real-analytic systems,” Systems Control Lett. 12 (1989): 205–211.
Delchamps, D.F., “Analytic stabilization and the algebraic Riccati equation,” Proc. IEEE Conf. Dec. and Control (1983): 1396–1401.
Gutman, P.O., “Stabilizing controllers for bilinear systems,” IEEE Trans. Autom. Control, 26 (1981): 917–922.
Jurdjevic, V. and J.P. Quinn, “Controllability and stability,” J.of Dif.Egs. 28 (1978): 381–389.
Kalouptsidis, N., and J. Tsinias, “Stability improvement of nonlinear systems by feedback,” IEEE Trans. Autom. Crt. 29 (1984): 346–367.
Kawski, M., “Stabilization of nonlinear systems in the plane,” Systems and Control Letters, 12 (1989): 169–176.
Koditschek, D.E., “Adaptive techniques for mechanical systems,” Proc.5th. Yale Workshop on Adaptive Systems, pp. 259–265, Yale University, New Haven, 1987.
Krasnoselskii, M.A., and P.P. Zabreiko, Geometric Methods of Nonlinear Analysis, Springer, Berlin, 1983.
Lee, K.K., and Arapostathis, A., “Remarks on smooth feedback stabilization of nonlinear systems,” Systems and Control Letters, 10 (1988): 41–44.
Marino R., “High-Gain Stabilization and Partial Feedback Linearization,” Proceedings of 25th CDC, Athens,IEEE Publ., 1986, pp.209–213
Massera, J.L., “Contributions to stability theory,” Annals of Math, 64 (1956): 182–206.
Massera, J.L., Erratum in Annals of Math, 68 (1958): 202.
Sastry, S.I., and A. Isidori, “Adaptive control of linearizable systems,” Memo UCB/ERL M87/53, March 1988, U.California, Berkeley.
Sira-Ramirez, H. “A geometric approach to pulse-width-modulated control in dynamical systems,” IEEE Trans. Automatic Control, 34 (1989): 184–187.
Slemrod, M., “Stabilization of bilinear control systems with applications to nonconservative problems in elasticity,” SIAM J.Control and Opt. 16 (1978): 131–141.
Sontag, E.D., “Nonlinear regulation: The piecewise linear approach,” IEEE Trans. Autom. Control AC-28(1981): 346–358.
Sontag, E.D., “Conditions for abstract nonlinear regulation,” Information and Control, 51 (1981): 105–127.
Sontag, E.D., “A Lyapunov-like characterization of asymptotic controllability,” SIAM J. Control and Opt., 21 (1983): 462–471.
Sontag, E.D., “Smooth stabilization implies coprime factorization,” IEEE Trans. Automatic Control, 34 (1989): 435–443.
Sontag, E.D., “A ‘universal’ construction of Artstein’s theorem on nonlinear stabilization,” Systems and Control Letters,13 (1989): No.2.
Sontag, E.D., “Further facts about input to state stabilization”, to appear in IEEE Trans. Automatic Control, 1990
Sontag, E.D., and H.J. Sussmann, “Remarks on continuous feedback,” Proc. IEEE Conf. Dec. and Control, Albuquerque, Dec.1980.
Sontag, E.D., and H.J. Sussmann, “Further comments on the stabilizability of the angular velocity of a rigid body,” Systems and Control Letters, 12 (1989): 213–217.
Sussmann, H.J., “Subanalytic sets and feedback control,” J.Diff.Eqs. 31 (1979): 31–52.
Sussmann, H.J., and P.V. Kokotovic, “The peaking phenomenon and the global stabilization of nonlinear systems,” Report 89–07, SYCON - Rutgers Center for Systems and Control, March 1989.
Tsinias, J., “Sufficient Lyapunovlike conditions for stabilization,” Math. of Control, Signals, and Systems 2 (1989): 343–357.
Utkin, V.I., Sliding Modes and Their Application in Variable Structure Systems, Mir, Moscow, 1978.
Vidyasagar, M., “Decomposition techniques for large-scale systems with nonadditive interactions: stability and stabilizability,” IEEE Trans. Autour. Ctr. 25 (1980): 773–779.
Vidyasagar, M., “On the stabilization of nonlinear systems using state detection,” IEEE Trans. Autom. Ctr. 25 (1980): 504–509.
Vidyasagar, M., Nonlinear Systems Analysis, Prentice-Hall, 1978.
Varaiya, P.P. and R. Liu, “Bounded-input bounded-output stability of nonlinear time-varying differential systems,” SIAM J.Control 4 (1966): 698–704.
Zabczyk J., “Some Comments on Stabilizability,” Applied Math Optimiz. 19 (1989): 1–9.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Sontag, E.D. (1990). Feedback Stabilization of Nonlinear Systems. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4484-4_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8839-8
Online ISBN: 978-1-4612-4484-4
eBook Packages: Springer Book Archive