Discontinuous Feedback and Universal Adaptive Stabilization

  • E. P. Ryan
Part of the Progress in Systems and Control Theory book series (PSCT, volume 6)


An adaptive stabilizer, universal for a class of nonlinear systems, is described. The stabilizer is of discontinuous feedback form and incorporates gains of Nussbaum type. The framework is that of differential inclusions and the stability analysis draws on an extension, to that framework, of LaSalle’s invariance principle for ordinary differential equations.


Differential Inclusion Invariance Principle Maximal Solution IEEE Trans Autom Control Uncontrolled System 
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  1. [1]
    B. Mârtensson, “The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization”, Systems and Control Letters, 6 (1985), 87–91.CrossRefGoogle Scholar
  2. [2]
    R.D. Nussbaum, “Some remarks on a conjecture in parameter adaptive control”, Systems and Control Letters, 3 (1983), 243–246.CrossRefGoogle Scholar
  3. [3]
    C.I. Byrnes and J.C.Willems. Byrnes and J.C.Willems, “Adaptive stabilization of multivariable linear systems”, Proc 23rd IEEE Conf. Decision and Control (1984), 1574–1577.Google Scholar
  4. [4]
    A.S. Morse, “A three-dimensional universal controller for the adaptive stabilization of any strictly proper minimum-phase system with relative degree not exceeding two”, IEEE Trans Autom Control, AC-30 (1985), 1188–1191.Google Scholar
  5. [5]
    J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, 1984.Google Scholar
  6. [6]
    F.H. Clarke, Optimization and Nonsmooth Analysis, WileyInterscience, 1983.Google Scholar
  7. [7]
    A.F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer, 1988.Google Scholar
  8. [8]
    J.P. LaSalle, The Stability of Dynamical Systems, Regional Conf. Series in Applied Math., SIAM, 1976.Google Scholar
  9. [9]
    J.A. Yorke, “Invariance for contingent equations”, in Mathematical Systems Theory and Economics II (W.H. Kuhn and G.P. Szegö, eds), 379–381, Springer-Verlag, 1969.Google Scholar
  10. [10]
    T.K.C. Peng, “Invariance and stability for bounded uncertain systems”, SIAM J Control, 10 (1972), 679–690.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • E. P. Ryan
    • 1
  1. 1.School of Mathematical SciencesUniversity of BathClaverton Down, BathUK

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