New Results on Nonlinear H-Control via Measurement Feedback

  • Alberto Isidori
Conference paper
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 1)


In the last few years, the solution of the H (sub)optimal control problem via state-space methods was developed by several authors (see, e.g. the prize-winning paper [1], the theses [2] [3] and the recent paper [4]). In the state-space formulation, the problem of minimizing the H norm (or, equivalently, the L 2gain) 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. [5], [6] and [7]).


Close Loop System State Feedback Differential Game Algebraic Riccati Equation Positive Definite Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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.MathSciNetCrossRefGoogle Scholar
  2. [2]
    A.A. Stoorvogel, The H∞ control problem: a state space approach, PhD thesis, Technical University Eindhoven, 1990.MATHGoogle Scholar
  3. [3]
    C. Scherer, The Riccati inequality and state-space H∞-optimal control, PhD thesis, University of Würzburg, 1990.Google Scholar
  4. [4]
    LR. Petersen, B.D.O. Anderson and E.A. Jonckheere, A first principles solution to the nonsingular H control problem, Int. J. of Robust and Nonlinear Control, 1:153–170, 1991.CrossRefGoogle Scholar
  5. [5]
    E.F. Mageirou and Y.C. Ho, Decentralized stabilization via game theoretic methods, Automatica, 13:888–896, 1977.CrossRefGoogle Scholar
  6. [6]
    G. Tadmor, Worst case design in time domain, Math. Control, Signals and Systems, 3:301–324, 1990.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    T. Basar and P. Bernhard, H∞-optimal control and related Minimax problems, Birkhauser, 1990.Google Scholar
  8. [8]
    J.A. Ball and J.W. Helton, H∞ optimal 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
  9. [9]
    A.J. Van der Schaft, A state-space approach to nonlinear H∞ control, Syst. and Contr. Lett., 16:1–8, 1991.CrossRefGoogle Scholar
  10. [10]
    A. Isidori, Feedback control of nonlinear systems, In Proc. of 1st European Control Conf., pages 1001–1012, Grenoble, France, July 1991.Google Scholar
  11. [11]
    A.J. Van der Schaft, L2-gain analysis of nonlinear systems and nonlinear H∞ control, IEEE Trans. Autom. Control, AC-37:770–784, 1992.Google Scholar
  12. [12]
    A. Isidori and A. Astolfi, Nonlinear H∞ control via measurement feedback, J. Math. Systems, Estimation and Control, 2:31–44, 1992.MathSciNetGoogle Scholar
  13. [13]
    A. Isidori and A. Astolfi, Disturbance attenuation and H∞ control via measurement feedback in nonlinear systems, IEEE Trans. Autom. Control, AC-37:1283–1293, 1992.MathSciNetCrossRefGoogle Scholar
  14. [14]
    J. Ball, J.W. Helton, and M.L. Walker, A variational approach to nonlinear H∞ control, Tech. memorandum, University of California at San Diego, August 1991.Google Scholar
  15. [15]
    A. Isidori, Dissipation inequalities in nonlinear H∞ control, Proc. 31th Conf. Decis. Contr., pages 3265–3270, Tucson, AZ, 1992.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Alberto Isidori
    • 1
    • 2
  1. 1.Departement of Computer and Systems ScienceUniversità di Roma “La Sapienza”RomeItaly
  2. 2.Department of Systems Sciences and MathematicsWashington UniversitySt. LouisUSA

Personalised recommendations