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Literature cited

  1. A. I. Lur'e, Some Nonlinear Problems in the Theory of Automatic Control [in Russian], Gostekhizdat, Moscow (1951).

    Google Scholar 

  2. V. A. Yakubovich, “The solution of some matrix inequalities occurring in the theory of automatic regulation,” Dokl. Akad. Nauk SSSR,143, No. 3, 1304–1307 (1962).

    Google Scholar 

  3. R. E. Kalman, “Lyapunov functions for the problem of Lur'e in automatic control,” Proc. Nat. Acad. Sci. USA,49, No. 2, 201–205 (1963).

    Google Scholar 

  4. V. M. Popov, Hyperstability of Automatic Systems [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  5. V. A. Yakubovich, “The frequency theorem in control theory,” Sib. Mat. Zh.,14, No. 2, 384–420 (1973).

    Google Scholar 

  6. A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, The Stability of Nonlinear Systems with Nonunique Equilibrium State [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  7. A. N. Churilov, “The frequency theorem and Lur'e's equation,” Sib. Mat. Zh.,20, No. 4, 854–868 (1979).

    Google Scholar 

  8. A. N. Churilov, “The solubility of certain matrix inequalities,” Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., Astron., No. 7, 51–55 (1980).

    Google Scholar 

  9. A. A. Voronov, Stability, Controllability and Observability [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  10. K. R. Meyer, “Lyapunov functions for the problems of Lur'e,” Proc. Nat. Acad. Sci. USA,53, No. 3, 501–503 (1965).

    Google Scholar 

  11. K. R. Meyer, “On the existence of Lyapunov functions for the problem of Lur'e,” SIAM J. Control, Ser. A,3, No. 3, 373–383 (1965).

    Google Scholar 

  12. M. D. Srinath, M. A. L. Thathacher, and H. K. Ramapriyan, “Absolute stability of systems with multiple nonlinearities,” Int. J. Control,7, No. 4, 365–375 (1968).

    Google Scholar 

  13. A. V. Zharkov, “The problem of the existence of a positive solution of Lur'e's equation,” Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., Astron., No. 13, 134–135 (1978).

    Google Scholar 

  14. W. A. Goppel, “Matrix quadratic equations,” Bull. Austral. Math. Soc,10, No. 3, 377–401 (1974).

    Google Scholar 

  15. P. Lancaster and L. Rodman, “Existence and uniqueness theorems for the algebraic Riccati equation,” Int. J. Control,32, No. 2, 285–310 (1980).

    Google Scholar 

  16. A. N. Churilov, “On solutions of a quadratic matrix equation,” in: Nonlinear Oscillations and Control Theory [in Russian], Vol. 2, Udmurtsk Univ., Izhevsk (1978), pp. 24–33.

    Google Scholar 

  17. F. R. Gantmakher, The Theory of Matrices, Chelsea Publ.

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Translated from Matematicheskie Zametki, Vol. 36, No. 5, pp. 725–732, November, 1984.

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Churilov, A.N. Solubility of matrix inequalities. Mathematical Notes of the Academy of Sciences of the USSR 36, 862–866 (1984). https://doi.org/10.1007/BF01139934

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  • DOI: https://doi.org/10.1007/BF01139934

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