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New algebraic conditions for controllability of neutral differential equations

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Abstract

The present paper is concerned with the study of the controllability of linear autonomous neutral functional differential equations in the state spaceR n×L 2([−h, 0],R n).Controllability conditions are based on an abstract evolution equation representation of the system. Useful algebraic criteria are derived. Starting from the abstract functional analytic framework, the analysis is carried down to the matrix theory level, through the crucial intermediate role of the theory of entire functions.

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References

  1. Banks, H. T., Jacobs, M. W., andLangenhop, C. E.,Characterization of the Controlled States in w (1)2 of Linear Hereditary Systems, SIAM Journal on Control and Optimization, Vol. 13, pp. 611–649, 1975.

    Google Scholar 

  2. Jacobs, M. Q., andLangenhop, C. E.,Criteria for Function Space Controllability of Linear Neutral Systems, SIAM Journal on Control and Optimization, Vol. 14, pp. 1009–1048, 1976.

    Google Scholar 

  3. O'Connor, P. A., andTarn, T. J.,On Function Space Controllability of Linear Neutral Systems, SIAM Journal on Control and Optimization, Vol. 21, pp. 306–329, 1983.

    Google Scholar 

  4. Rodas, H. R., andLangenhop, C. E.,A Sufficient Condition for Function Space Controllability of a Linear Neutral System, SIAM Journal on Control and Optimization, Vol. 16, pp. 429–435, 1978.

    Google Scholar 

  5. Salamon, D.,Control and Observation of Neutral Systems, Pitman Verlag, Boston, Massachusetts, 1984.

    Google Scholar 

  6. Manitius, A., andTriggiani, R.,Sufficient Conditions for Function Space Controllability and Feedback Stabilizability of Linear Retarded Systems, IEEE Transactions on Automatic Control, Vol. AC-23, pp. 659–665, 1978.

    Google Scholar 

  7. Manitius, A., andTriggiani, R.,Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions, Université de Montréal, Centre de Recherches Mathematiques, Report No. CRM-605, 1976.

  8. Kappel, F.,Approximation of Neutral Functional Differential Equations in the State Space R n × L2,Colloquia Mathematica Societatis János Bolyai, Vol. 30, Qualitative Theory of Differential Equations, Szeged, Hungary, 1979.

    Google Scholar 

  9. Gantmacher, F. K.,Matrizenrechnung, I, VEB Deutscher Verlag der Wissenschaften, Berlin, Germany, 1958.

    Google Scholar 

  10. Doetsch, G.,Handbuch der Laplace-Transformation, I–III, Birkhäuser Verlag, Basel, Switzerland, 1950.

    Google Scholar 

  11. Ahlfors, L. V.,Complex Analysis, McGraw-Hill Book Company, New York, New York, 1966.

    Google Scholar 

  12. Fuchs, E., Entartung bei Linearen Autonomen Funktional-Differential-gleichungen vom Neutralen Typ, Mitteilungen aus dem Forschungsschwerpunkt Simulation und Optimierung Deterministischer und Stochastischer Dynamischer Systeme, Hochschule der Bundeswehr München, Neubiberg, Germany, 1981.

    Google Scholar 

  13. Faddejew, D. K., andFaddejewa, W. N.,Numerische Methoden der Linearen Algebra, R. Oldenbourg Verlag, München, Germany, 1964.

    Google Scholar 

  14. Lancaster, P.,Theory of Matrices, Academic Press, New York, New York, 1969.

    Google Scholar 

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Communicated by L. Cesari

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Reinbacher, H. New algebraic conditions for controllability of neutral differential equations. J Optim Theory Appl 54, 93–111 (1987). https://doi.org/10.1007/BF00940406

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