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Controllability, observability and stability

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References

  1. Banks, H.T., Jacobs, M.Q. and Langenkop, C.E. Characterisations of the controlled states in W 12 of linear hereditary systems, SIAM J. Control, 13 (1975), pp. 611–649.

    Google Scholar 

  2. Benchimol, C.D. The stabilizability of infinite dimensional linear time invariant systems, Thesis UCLA, 1977.

    Google Scholar 

  3. Butkovskii, A.G. Theory of optimal control of distributed parameter systems, Elsevier, New York, 1969.

    Google Scholar 

  4. Curtain, R.F. and Pritchard, A.J. A semigroup approach to infinite dimensional systems theory, Proceedings of the IMA Symposium on Recent Theoretical Developments in Control, Leicester, 1976.

    Google Scholar 

  5. Datko, R. Extending a theorem of A.M. Liapunov to Hilbert space, J. Math. Anal. Appl., 32 (1970), pp. 610–616.

    Google Scholar 

  6. Datko, R. Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3 (1972), pp. 428–445.

    Google Scholar 

  7. Delfour, M.C. and Mitter, S.K. Controllability, observability and optimal feedback control of affine hereditary differential systems, SIAM J. Control, 10 (1972), pp. 298–328.

    Google Scholar 

  8. Delfour, M.C. and Mitter, S.K. Controllability and observability for infinite dimensional systems, SIAM J. Control, 10 (1972), pp. 329–333.

    Google Scholar 

  9. Dolecki, S. and Russell, D. A general theory of observation and control, SIAM J. Control, 15 (1977), pp. 185–220.

    Google Scholar 

  10. Fattorini, H.O. On control in finite time of differential equations in Banach space, Comm. Pure App. Maths, XIX (1966), pp. 17–34.

    Google Scholar 

  11. Fattorini, H.O. Some remarks on complete controllability, SIAM J. Control, 4 (1966), pp. 686–694.

    Google Scholar 

  12. Fattorini, H.O. On complete controllability of linear systems, J. Diff. Eqns., 3 (1967), pp. 391–402.

    Google Scholar 

  13. Fattorini, H.O. Controllability of higher order linear systems in mathematical theory of control, Eds. Balakrishnan, A.V. and Neustad, L.W., Academic Press, 1967

    Google Scholar 

  14. Fattorini, H.O. and Russell, D.L. Exact controllability theorems for linear parabolic equations in one space dimension, Archiv. Rat. Mech. Anal., 43 (1971), pp.272–292.

    Google Scholar 

  15. Gabasov, R. and Curakova, S.V. The theory of controllability of linear systems with delay lags, Eng. Cybernetics, 4 (1969), pp.16–27.

    Google Scholar 

  16. Halanay, A. On the controllability of linear difference-differential systems in lecture notes in operations research and mathematical economics, 12, Springer Verlag, 1970.

    Google Scholar 

  17. Helton, J.W. Systems with infinite dimensional state space: the Hilbert space approach, Proc. IEEE, 64 (1976), pp.145–160.

    Google Scholar 

  18. Hille, E. and Phillips, R.S. Functional analysis and semigroups, Publ. Amer. Math. Soc., 1957.

    Google Scholar 

  19. Kirrillova, F.M. and Curakova, S.V. Relative controllability of systems with time lag, Dokl. Akad. Nauk. USSR, 176 (1967), pp.1260–1263.

    Google Scholar 

  20. Kobayashi, T. Initial state determination for distributed parameter systems, SIAM J. Control, 14 (1976), pp.934–944.

    Google Scholar 

  21. Lukes, D.L. Stabilizability and optimal control, Funkial. Ekvac., 2 (1968), pp.39–50.

    Google Scholar 

  22. Manitius, A. Optimal control of hereditary systems, Control Theory and Topics in Functional Analysis Vol III, International Atomic Energy Agency, (1976), pp.43–178.

    Google Scholar 

  23. Manitius, A. and Triggiani, R. Function space controllability for linear retarded systems: a derivation from abstract operator conditions, International Report CRM 605, Centre de Recherches Mathematiques, Universite de Montreal, 1976.

    Google Scholar 

  24. Manitius, A. and Triggiani, R. Sufficient conditions for function space controllability and feedback stabilizability of linear retarded systems, Proc. IEEE Conference on Decision and Control, 1976.

    Google Scholar 

  25. Manitius, A. and Triggiani, R. Controllability, observability and stabilizability of retarded systems, Proc. IEEE Conference on Decision and Control, 1976.

    Google Scholar 

  26. Olbrot, A.W. On controllability of linear systems with time delays in the control, IEEE Trans. Aut. Control, AC 16 (1972), pp.664–666.

    Google Scholar 

  27. Pandolfi, L. On feedback stabilization of functional differential equations, Boll. UHI 4, 11 Supplemento al Fascicolo 3, Giugno, Ser IV Vol XI (1975), pp.626–635.

    Google Scholar 

  28. Popov, V.M. Pointwise degeneracy of linear time invariant delay-differential equations, J. Diff. Eqns., 11 (1972), pp. 541–561.

    Google Scholar 

  29. Pritchard, A.J. Stability and control of distributed systems, Proc. IEE, (1969), pp.1433–1438.

    Google Scholar 

  30. Pritchard, A.J. and Triggiani, R. Stabilizability in Banach space, Control Theory Centre Report No.35, University of Warwick, 1974.

    Google Scholar 

  31. Pritchard, A.J. and Zabczyk, J. Stability and stabilizability of infinite dimensional systems, Control Theory Centre Report No.70, University of Warwick, 1977.

    Google Scholar 

  32. Rolewicz, S. On universal time for controllability of time-depending linear control systems, Studia Mathematica, 59 (1976), pp.133–138.

    Google Scholar 

  33. Russek, A. On relations between exact controllability and rank condition, Preprint Inst. Mathematics, Warsaw, 1975.

    Google Scholar 

  34. Russell, D.L. Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory, J. Math. Anal. Appl., 40 (1972), pp.336–368.

    Google Scholar 

  35. Russell, D.L. Linear stabilization of the linear oscillator in Hilbert space, J. Math. Anal. Appl., 25 (1969), pp.663–675.

    Google Scholar 

  36. Russell, D.L. Problems of control and stabilization for partial differential equations, Proc. 6th IFAC Congress, Boston, 1975.

    Google Scholar 

  37. Sakawa, Y. Controllability for partial differential equations of parabolic type, SIAM J. Control, 12 (1974), pp.389–400.

    Google Scholar 

  38. Sakawa, Y. Observability and related problems for partial differential equations of parabolic type, SIAM J. Control, 13 (1975), pp.14–27.

    Google Scholar 

  39. Slemrod, M. A note on complete controllability and stabilizability of linear control systems in Hilbert space. SIAM J. Control, 12 (1974), pp.500–508.

    Google Scholar 

  40. Slemrod, M. The linear stabilization problem in Hilbert space, J. Functional Anal., 11 (1972), pp.334–345.

    Google Scholar 

  41. Triggiani, R. Controllability and observability in Banach spaces with bounded operators, SIAM J. Control, 13 (1975), pp.462–491.

    Google Scholar 

  42. Triggiani, R. On a lack of exact controllability for mild solutions in Banach space, J. Math. Anal. Appl., 50 (1975), pp.438–446.

    Google Scholar 

  43. Triggiani, R. Extension of rank conditions for controllability and observability to Banach spaces and unbounded operators, SIAM J. Control, 14 (1976), pp.313–338.

    Google Scholar 

  44. Triggiani, R. On the stabilization problem in Banach space, J. Math. Anal. Appl., 52 (1975), pp.383–403.

    Google Scholar 

  45. Triggiani, R. On the relationship between first and second order controllable systems in Banach space, Proc. IFIP Conference on Identification and Modelling of Distributed Parameter Systems, Rome, 1976.

    Google Scholar 

  46. Tsujioka, K. Remarks on controllability of second order evolution equations in Hilbert spaces, SIAM J. Control, 8, (1970), pp.90–99.

    Google Scholar 

  47. Wang, P.K.C. On feedback control of distributed parameter systems, Int. J. Control, 3 (1966), pp.255–273.

    Google Scholar 

  48. Wang, P.K.C. Feedback stabilization of distributive systems with applications to plasma stabilization, Instability of Continuous Systems, Ed. H. Leipholz, Springer Verlag, 1971.

    Google Scholar 

  49. Weiss, L. On the controllability of delay-differential systems, SIAM J. Control, 5 (1967), pp.575–587.

    Google Scholar 

  50. Wiberg, D.M. Feedback control of linear distributed systems, Trans. ASME J. Basic Eng., 89 (1967), pp.379–384.

    Google Scholar 

  51. Zabczyk, J. Remarks on the control of discrete time distributed parameter systems, SIAM J. Control, 12 (1974), pp.721–735.

    Google Scholar 

  52. Zabczyk, J. Complete stabilizability implies exact controllability, Seminarul de Ecuatti Functionale, Universitatea din Timosoara, Rumania, 1976.

    Google Scholar 

  53. Zabczyk, J. A note on Co semigroups, Bull. l'Acad. Pol. de Sc. Serie Math., 23 (1975), pp.895–898.

    Google Scholar 

  54. Zabczyk, J. Remarks on the algebraic Riccati equation in Hilbert space, Appl. Math. Optimisation, 3 (1976), pp.383–403.

    Google Scholar 

  55. Zmood, R.B. The Euclidean space controllability of control systems with delay, SIAM J. Control, 12 (1974), pp.609–623.

    Google Scholar 

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Ruth F. Curtain Anthony J. Pritchard

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(1978). Controllability, observability and stability. In: Curtain, R.F., Pritchard, A.J. (eds) Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006764

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  • DOI: https://doi.org/10.1007/BFb0006764

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