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Generalization of the frequency theorem in the case of an unbounded observation operator and its application to absolute stability problems

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Literature Cited

  1. V. A. Yakubovich, “The frequency theorem for the case in which the state space and the control space are Hilbert spaces, and its application to some problems of synthesis of optimal control. I, II,” Sib. Mat. Zh.,15, No. 3, 639–668 (1974);16, No. 5, 1081–1102 (1975).

    Google Scholar 

  2. A. L. Likhtarnikov and V. A. Yakubovich, “A frequency theorem for continuous one-parameter semigroups,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 4, 895–911 (1977).

    Google Scholar 

  3. V. A. Brusin, “Lur'e equations in Hilbert space and their solvability,” Prikl. Mat. Mekh.,40, No. 5, 947–956 (1976).

    Google Scholar 

  4. V. G. Deich, “Optimal stabilization of infinite-dimensional systems with an unbounded quality functional,” Sib. Mat. Zh.,28, No. 1, 99–106 (1987).

    Google Scholar 

  5. A. L. Likhtarnikov, “Absolute stability criteria for nonlinear operator equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 5, 1064–1083 (1977).

    Google Scholar 

  6. V. A. Brusin, “Existence of a global Lyapunov functional for some classes of nonlinear distributed systems,” Prikl. Mat. Mekh.,40, No. 6, 1135–1142 (1976).

    Google Scholar 

  7. V. G. Deich, “Discrete approximation of stabilizing feedback in systems with distributed parameters,” Avtomat. Telemekh., No. 8, 36–45 (1987).

    Google Scholar 

  8. S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  9. W. Rudin, Functional Analysis, McGraw-Hill, New York (1973).

    Google Scholar 

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Authors
  1. V. G. Deich
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Deceased.

Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 44–52, July–August, 1989.

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Deich, V.G. Generalization of the frequency theorem in the case of an unbounded observation operator and its application to absolute stability problems. Sib Math J 30, 535–542 (1989). https://doi.org/10.1007/BF00971752

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  • DOI: https://doi.org/10.1007/BF00971752

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