Attenuation of Disturbances in Nonlinear Control Systems

  • Alberto Isidori
Part of the Progress in Systems and Control Theory book series (PSCT, volume 12)


In the last few years, the solution of the H (sub)optimal control problem via state-space methods was developed by several authors (for a rather comprehensive coverage of this subject the reader may consult the paper [1] and the theses [2] [3]). In the state-space formulation, the problem of minimizing the H norm (or, equivalently, the L 2 gain) of a closed loop system is viewed as a two-person, zero sum, differential game and, thus, the existence of the desired controller can be related to the existence of a solution of the algebraic Riccati equations arising in linear quadratic differential game theory (see, e.g. [4], [5] and [6]).


Nonlinear System Hamiltonian System Close Loop System Invariant Manifold Differential Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    J.C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis, State space solutions to standard H2 and H. control problems, IEEE Trans. Autom. Control, AC-34: 831–846, 1989.Google Scholar
  2. [2]
    A.A. Stoorvogel, The H. control problem: a state space approach, PhD thesis, Technical University Eindhoven, 1990.Google Scholar
  3. [3]
    C. Scherer, The Riccati inequality and state-space H.-optimal control, PhD thesis, University of Würzburg, 1990.Google Scholar
  4. [4]
    E.F. Mageirou and Y.C. Ho, Decentralized stabilization via game theoretic methods, Automatica, 13: 888–896, 1977.CrossRefGoogle Scholar
  5. [5]
    G. Tadmor, Worst case design in time domain, Math. Control, Signals and Systems, 3: 301–324, 1990.CrossRefGoogle Scholar
  6. [6]
    T. Basar and P. Bernhard, H.-optimal control and related Minimax problems, Birkhauser, 1990.Google Scholar
  7. [7]
    J.A. Ball and J.W. Helton, H. control for nonlinear plants: connection with differential games, In Proc. of 28th Conf Decision and Control, pages 956–962, Tampa, FL, December 1989.CrossRefGoogle Scholar
  8. [8]
    A.J. Van der Schaft, A state-space approach to nonlinear H. control, Syst. and Contr. Lett., 16: 1–8, 1991.CrossRefGoogle Scholar
  9. [9]
    A. Isidori, Feedback control of nonlinear systems, In Proc. of 1st European Control Conf., Grenoble, France, July 1991.Google Scholar
  10. [10]
    A.J. Van der Schaft, L2-gain analysis of nonlinear systems and nonlinear H. control, Tech. Memorandum 969, Universiteit Twente, 1991.Google Scholar
  11. [11]
    A. Isidori and A. Astolfi, Nonlinear H. control via measurement feedback, J. Math. Systems, Estimation and Control, 2:to appear, 1992.Google Scholar
  12. [12]
    B.D. Anderson, An algebraic solution to the spectral factorization problem, IEEE Trans. Autom. Control, AC-12: 410–414, 1967.Google Scholar
  13. [13]
    R.W. Brockett, Finite dimensional linear systems, Wiley, 1970.Google Scholar
  14. [14]
    J.C. Willems, Least square optimal control and the algebraic riccati equation, IEEE Trans. Autom. Control, AC-16: 621–634, 1971.Google Scholar
  15. [15]
    P.J. Moylan, Implications of passivity in a class of nonlinear systems, IEEE Trans. Autom. Control, AC-19: 373–381, 1974.Google Scholar
  16. [16]
    D. Hill and P.J. Moylan, The stability of nonlinear dissipative systems, IEEE Trans. Autom. Control, AC-21: 708–711, 1976.Google Scholar
  17. [17]
    J.C. Willems, Dissipative dynamical systems, Arch. Rational Mechanics and Analysis, 45: 321–693, 1972.CrossRefGoogle Scholar
  18. [18]
    C.I. Byrnes and A. Isidori, Steady state response, separation principle and the output regulation of nonlinear systems, In Proc. of 28th Conf. Decision and Control, pages 2247–2251, Tampa, FL, December 1989.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Alberto Isidori
    • 1
    • 2
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.Department of Systems Science and MathematicsWashington UniversitySt. LouisUSA

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