Literature Cited
V. A. Yakubovich, “A linear-quadratic optimization problem and the frequency theorem for periodic systems. I,” Sib. Mat. Zh.,27, No. 4, 181–200 (1986).
I. M. Gel'fand and V. B. Lidskii, “The structure of domains of stability of linear canonical systems of differential equations with periodic coefficients,” Usp. Mat. Nauk,10, No. 1, 3–40 (1955).
V. A. Yakubovich, “Problems on the stability of solutions of systems of two linear differential equations in canonical form with periodic coefficients,” Mat. Sb.,37, 21–67 (1955).
V. A. Yakubovich, “The structure of the group of symplectic matrices and the structure of sets of unstable canonical systems with periodic coefficients,” Mat. Sb.,44, No. 3, 313–352 (1958).
V. I. Arnol'd, “The characteristics of a class under quantization conditions,” Funkts. Anal. Prilozh.,1, No. 1, 1–14 (1967).
S. Bittanti and P. Bolzern, “Stabilizability and detectability of linear periodic systems,” Systems Control Lett.,6, 141–145 (1983).
V. A. Yakubovich, “The frequency theorem for periodic systems in the theory of analytic regulator design,” in: The Method of Lyapunov Functions in Analysis of Dynamic Systems [in Russian], Nauka, Novosibirsk (1987), pp. 281–290.
V. A. Yakubovich, “Arguments on the group of symplectic matrices,” Mat. Sb.,55, 255–280 (1961).
V. A. Yakubovich, “Oscillatory properties of canonical equations,” Mat. Sb.,56, No. 1, 3–42 (1962).
V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Applications [in Russian], Nauka, Moscow (1972).
I. M. Glazman, Direct Methods for Qualitative Spectral Analysis of Singular Differential Operators [in Russian], GIFML, Moscow. (1963).
V. A. Yakubovich, “Applications of the theory of linear periodic Hamiltonian systems to problems on absolute stability of nonlinear systems with periodic nonstationary linear parts,” Vestn. LGU, Ser. 1, No. 3, 55–60 (1987).
V. A. Yakubovich, “The method of the small parameter for canonical systems with periodic coefficients,” Prikl. Mat. Mekh.,23, No. 1, 15–34 (1959).
V. I. Arnol'd “The Sturm theorem and symplectic geometry,” Funkts. Anal. Prilozh.,19, No. 4, 1–10 (1985).
V. P. Maslow, Perturbation Theory and Asymptotic Methods [in Russian], Moscow State Univ. (1965).
Ch. J. Byrnes, “On a theorem of Hermite and Hurwitz,” Linear Algebra Its Appl.,50, 61–101 (1983).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 6, pp. 176–191, November–December, 1990.
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Yakubovich, V.A. Linear-quadratic optimization problem and the frequency theorem for periodic systems. II. Sib Math J 31, 1027–1039 (1990). https://doi.org/10.1007/BF00970068
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DOI: https://doi.org/10.1007/BF00970068