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Block noninteracting control with stability via static state feedback

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Abstract

Necessary and sufficient conditions for the existence of a static state feedback that achieves noninteraction and internal stability are obtained. This is accomplished by first characterizing the set of all controllability subspaces (distributions) that can arise as solutions to the noninteracting control problem. This characterization is then used to identify a fixed internal dynamics that is common to every noninteractive closed loop. The stability properties of this dynamics is shown to be the key factor in the problem of achieving noninteracting control with internal stability.

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References

  • [D] J. Descusse, Un example d’application des méthodes géomètriques: Le problème du découplage, inOutils et modèles mathématiques pour l’automatique, l’analyse de systèmes et le traitement du signal, Vol. 1 (I. D. Landau, ed.), pp. 53–63, Centre National de la Recherche Scientific, Paris, 1981.

    Google Scholar 

  • [DLM] J. Descusse, J. F. Lafay, and M. Malabre, On the structure at infinity of linear block-decouplable systems: the general case,IEEE Trans. Automat. Control,28 (1983), 1115–1118.

    Article  MathSciNet  Google Scholar 

  • [DM] J. Descusse and C. H. Moog, Decoupling with dynamic compensation for strong invertible affine nonlinear systems,Internat. J. Control 42 (1985), 1387–1398.

    MathSciNet  Google Scholar 

  • [F] M. Fliess, A new approach to the noninteracting control problem in nonlinear system theory,Proceedings of the 23rd Allerton Conference, Monticello, IL, 1985, pp. 123–129.

  • [G1] E. G. Gilbert, The decoupling of multivariable systems by state feedback,SIAM J. Control, Optim. 7 (1969), 50–63.

    Article  Google Scholar 

  • [G2] J. W. Grizzle, Local input-output decoupling of discrete-time non-linear systems,Internat J. Control,43 (1986), 517–530.

    MathSciNet  Google Scholar 

  • [H1] I. J. Ha, The standard decomposed system and noninteracting feedback control of nonlinear systems, Preprint (to appear inSIAM J. Control Optim.).

  • [H2] I. J. Ha, Nonlinear Decoupling Theory with Applications to Robotics, Ph.D. Dissertation, CRIM Report RSD-TR-8-85, University of Michigan, Ann Arbor, 1985.

    Google Scholar 

  • [HG] I. J. Ha and E. G. Gilbert, A complete characterization of decoupling control laws for a general class of nonlinear systems,IEEE Trans. Automat. Control,31 (1986), 823–830.

    Article  MathSciNet  Google Scholar 

  • [H3] R. M. Hirschorn, (A.B)-invariant distributions and disturbance decoupling of non-linear systems,SIAM J. Control Optim.,19 (1981), 1–19.

    Article  MathSciNet  Google Scholar 

  • [I] A. Isidori,Nonlinear Control Systems: An Introduction, Lecture Notes in Control and Information Sciences, Vol. 72, Springer-Verlag, Berlin, 1985.

    Book  MATH  Google Scholar 

  • [IG] A. Isidori and J. W. Grizzle, Fixed modes and nonlinear noninteracting control with stability,IEEE Trans. Automat. Control,33 (1988), 907–914.

    Article  MathSciNet  Google Scholar 

  • [IKGM] A. Isidori, A. J. Krener, C. Gori-Giorgi, and S. Monaco, Nonlinear decoupling via feedback: a differential geometric approach,IEEE Trans. Automat. Control,26 (1981), 331–345.

    Article  MathSciNet  Google Scholar 

  • [MW] A. S. Morse and W. M. Wonham, Status of noninteracting control,IEEE Trans. Automat. Control,16 (1971), 568–581.

    Article  MathSciNet  Google Scholar 

  • [NR] H. Nijmeijer and W. Respondek, Decoupling via dynamic compensation for nonlinear control systems,Proceedings of the 25th IEEE Conference on Decision and Control, Athens, 1986, pp. 192–197.

  • [NS1] H. Nijmeijer and J. M. Schumacher, Zeros at infinity for affine nonlinear systems,IEEE Trans. Automat. Control,30 (1985), 566–573.

    Article  MathSciNet  Google Scholar 

  • [NS2] H. Nijmeijer and J. M. Schumacher, The regular local noninteracting control problem for nonlinear control systems,Siam J. Control Optim.,24 (1986), 1232–1245.

    Article  MathSciNet  Google Scholar 

  • [W] W. M. Wonham,Linear Multivariable Control: A Geometric Approach, 2nd edn., Springer-Verlag, New York, 1979.

    MATH  Google Scholar 

  • [WM] M. H. Wonham and A. S. Morse, Decoupling and pole assignment in linear multivariable systems: a geometric approach,SIAM J. Contral Optim.,8 (1970), 1–18.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, and Computer Science, University of Michigan, 48109-2122, Ann Arbor, Michigan, USA

    J. W. Grizzle

  2. Dipartimento di Informatica e Sistemistica, Università di Roma, La Sapienza, Roma, Italy

    A. Isidori

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  1. J. W. Grizzle
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  2. A. Isidori
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Grizzle, J.W., Isidori, A. Block noninteracting control with stability via static state feedback. Math. Control Signal Systems 2, 315–341 (1989). https://doi.org/10.1007/BF02551275

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  • DOI: https://doi.org/10.1007/BF02551275

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