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Disturbance decoupling and invariant subspaces for delay systems

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Abstract

In this paper we consider the disturbance decoupling problem for distributed parameter systems, with special attention to the case of delay systems. We present several examples which illustrate the difficulties of the infinite dimensional theory for the case of general distributed parameter systems and for the case of delay systems. In this last case we single out a class of subspaces whose invariant properties are easily characterized and which seems to be interesting from the point of view of the applications.

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References

  1. Balakrishnan AV (1976) Applied Functional Analysis, Springer-Verlag, New York

    Google Scholar 

  2. Callier FM, Desoer CA (1980) Stabilization, tracking and disturbance rejection in multivariable convolution systems, Annales de la Soc Scient de Bruxelles 94:7–51

    Google Scholar 

  3. Curtain R Invariance concepts in infinite dimensions, SIAM J. Control Opt, to appear

  4. Curtain R Disturbance Decoupling for Distributed Systems by Boundary Control, 2nd International Conference on Control Theory for Distributed Parameter Systems and Applications, Vorau, July 1984 Springer-Verlag Berlin, to appear

    Google Scholar 

  5. Davies B (1978) Integral Transformations and their Applications, Springer-Verlag, New York

    Google Scholar 

  6. Delfour MC (1980) The largest class of hereditary systems defining aC 0-semigroup on the product space, Canadian J Math 32:969–978

    Google Scholar 

  7. Delfour MC, Manitius A (1980) The structural operatorF and its role in the theory of retarded systems I, II, J Math Analysis Appl 73:466–491, 74:359–381

    Google Scholar 

  8. Desoer, CA, Wang YT (1980) Linear Time-Invariant Robust Servomechanism Problem: a Selfcontained Exposition. In: Leondes CT (ed) Advances in Control and Dynamical Systems, Academic Press, New York

    Google Scholar 

  9. Hautus MLJ (1980) (A, B)-invariant and stabilizability subspaces, a frequency domain description, Automatica, 16:703–707

    Google Scholar 

  10. Kato T (1966) Perturbation Theory for Linear Operators, Springer-Verlag, Berlin

    Google Scholar 

  11. Manitius A (1981) Necessary and sufficient conditions of approximate controllability for general linear retarded systems, SIAM J Control Opt 19:516–535

    Google Scholar 

  12. Manitius A, Triggiani R (1978) Function space controllability of linear retarded systems: a derivation from abstract operator conditions, SIAM J Control Opt 16:599–645

    Google Scholar 

  13. Morse AS (1973) Structural invariants of linear multivariable systems, SIAM J Control 11:446–464

    Google Scholar 

  14. Pandolfi L (1982) Some Observations about the Structure of Systems with Delays. In: Bensoussan A, Lions JL (eds) Analysis and Optimization of Systems, Springer-Verlag, Berlin

    Google Scholar 

  15. Pandolfi L (1982) The transmission zeros of systems with delays, International J Control 36:959–976

    Google Scholar 

  16. Pandolfi L (1983) The Pole and Zero Structure of a Class of Linear Systems. In: Kappel F, Kunish K, Schappacher (eds) Control Theory for Distributed Parameter Systems and Applications, Springer Verlag, Berlin

    Google Scholar 

  17. Pandolfi L, Tandem Connection of Systems with Delays, 2nd International Conference on Control Theory for Distributed Parameter Systems and Applications, Vorau, July 1984

  18. Salamon D (1982) On Control and Observation of Neutral Systems, Dissertation, Bremen

  19. Schmidt EJP, Stern RJ (1980) Invariance theory for infinite dimensional linear control systems, Applied Math Opt 6:113–122

    Google Scholar 

  20. Schumacher JM (1983) Dynamic feedback in finite- and infinite-dimensional systems, Mathematisch Centrum, Amsterdam, Holland

    Google Scholar 

  21. Watanabe K, Ito M (1981) A process-model control for linear systems with delay, IEEE Trans Automatic Control, 26:1261–1269

    Google Scholar 

  22. Watanabe K, Sato M (1984) A process-model control for multivariable systems with multiple delays in inputs and outputs subject to unmeasurable disturbances, Int J Control 39:1–17

    Google Scholar 

  23. Wonham WM (1979) Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10100, Torino, Italia

    L. Pandolfi

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  1. L. Pandolfi
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This paper has been written according with the research programs of the GNAFA-CNR, with financial support from the Ministero della Pubblica Istruzione.

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Pandolfi, L. Disturbance decoupling and invariant subspaces for delay systems. Appl Math Optim 14, 55–72 (1986). https://doi.org/10.1007/BF01442228

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  • DOI: https://doi.org/10.1007/BF01442228

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