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Volumn 2003, Issue 16, 2003, Pages 1027-1041

On a criterion of Yakubovich type for the absolute stability of nonautonomous control processes

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EID: 0346181968     PISSN: 01611712     EISSN: None     Source Type: Journal    
DOI: 10.1155/S0161171203201095     Document Type: Article
Times cited : (8)

References (25)
  • 1
    • 0003728853 scopus 로고
    • Translated by E. Polak, Holden-Day, California, MathSciNet. Zentralblatt für Mathematik
    • M. A. Aizerman and F. R. Gantmacher, Absolute Stability of Regulator Systems, Translated by E. Polak, Holden-Day, California, 1964. MathSciNet. Zentralblatt für Mathematik.
    • (1964) Absolute Stability of Regulator Systems
    • Aizerman, M.A.1    Gantmacher, F.R.2
  • 2
    • 0003190051 scopus 로고
    • On a characteristic class entering in a quantum condition
    • V. Arnold, On a characteristic class entering in a quantum condition, Funct. Anal. Appl. 1 (1969), 1-14.
    • (1969) Funct. Anal. Appl. , vol.1 , pp. 1-14
    • Arnold, V.1
  • 4
    • 0002709196 scopus 로고
    • Dichotomies in stability theory
    • Springer-Verlag, Berlin, MathSciNet. Zentralblatt für Mathematik
    • W. A. Coppel, Dichotomies in Stability Theory, Lecture Notes in Mathematics, vol. 629, Springer-Verlag, Berlin, 1978. MathSciNet. Zentralblatt für Mathematik.
    • (1978) Lecture Notes in Mathematics , vol.629
    • Coppel, W.A.1
  • 5
    • 17844406719 scopus 로고    scopus 로고
    • On the Yakubovich frequency theorem for linear non-autonomous control processes
    • to appear in
    • R. Fabbri, R. Johnson, and C. Núñez, On the Yakubovich Frequency Theorem for linear non-autonomous control processes, to appear in Discrete Contin. Dynam. Systems.
    • Discrete Contin. Dynam. Systems.
    • Fabbri, R.1    Johnson, R.2    Núñez, C.3
  • 6
    • 85006238033 scopus 로고    scopus 로고
    • The rotation number for non-autonomous linear Hamiltonian systems I: Basic properties
    • to appear in
    • R. Fabbri, R. Johnson, and C. Núñez, The rotation number for non-autonomous linear Hamiltonian systems I: basic properties, to appear in Z. Angew. Math. Phys.
    • Z. Angew. Math. Phys.
    • Fabbri, R.1    Johnson, R.2    Núñez, C.3
  • 7
    • 85006238034 scopus 로고    scopus 로고
    • The rotation number for non-autonomous linear Hamiltonian systems II: The Floquent coefficient
    • to appear in
    • R. Fabbri, R. Johnson, and C. Núñez, The rotation number for non-autonomous linear Hamiltonian systems II: The Floquent coefficient, to appear in Z. Angew. Math. Phys.
    • Z. Angew. Math. Phys.
    • Fabbri, R.1    Johnson, R.2    Núñez, C.3
  • 8
    • 0000809966 scopus 로고
    • $m$-functions and Floquet exponents for linear differential systems
    • MathSciNet. Zentralblatt für Mathematik
    • R. Johnson, $m$-functions and Floquet exponents for linear differential systems, Ann. Mat. Pura Appl. (4) 147 (1987), 211-248. MathSciNet. Zentralblatt für Mathematik.
    • (1987) Ann. Mat. Pura Appl. (4) , vol.147 , pp. 211-248
    • Johnson, R.1
  • 9
    • 33748820691 scopus 로고    scopus 로고
    • Controllability, stabilization and the regulator problem for random differential systems
    • MathSciNet
    • R. Johnson and M. Nerurkar, Controllability, stabilization and the regulator problem for random differential systems, Mem. Amer. Math. Soc. 136 (1998), no. 646, 1-48. MathSciNet.
    • (1998) Mem. Amer. Math. Soc. , vol.136 , Issue.646 , pp. 1-48
    • Johnson, R.1    Nerurkar, M.2
  • 10
    • 0000302024 scopus 로고
    • Lyapunov functions for the problem of Lure in automatic control
    • MathSciNet. Zentralblatt für Mathematik
    • R. E. Kalman, Lyapunov functions for the problem of Lure in automatic control, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 201-205. MathSciNet. Zentralblatt für Mathematik.
    • (1963) Proc. Nat. Acad. Sci. U.S.A. , vol.49 , pp. 201-205
    • Kalman, R.E.1
  • 12
    • 0004500720 scopus 로고
    • Linear differential equations and function spaces
    • Academic Press, London, MathSciNet. Zentralblatt für Mathematik
    • J. L. Massera and J. J. Schaffer, Linear Differential Equations and Function Spaces, Pure and Applied Mathematics, vol. 21, Academic Press, London, 1966. MathSciNet. Zentralblatt für Mathematik.
    • (1966) Pure and Applied Mathematics , vol.21
    • Massera, J.L.1    Schaffer, J.J.2
  • 13
    • 0012917563 scopus 로고
    • Qualitative theory of differential equations
    • Princeton University Press, New Jersey, MathSciNet. Zentralblatt für Mathematik
    • V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton Mathematical Series, no. 22, Princeton University Press, New Jersey, 1960. MathSciNet. Zentralblatt für Mathematik.
    • (1960) Princeton Mathematical Series , vol.22
    • Nemytskii, V.V.1    Stepanov, V.V.2
  • 14
    • 0004500735 scopus 로고    scopus 로고
    • Ergodic properties and rotation number for linear Hamiltonian systems
    • CrossRef. MathSciNet. Zentralblatt für Mathematik
    • S. Novo, C. Núñez, and R. Obaya, Ergodic properties and rotation number for linear Hamiltonian systems, J. Differential Equations 148 (1998), no. 1, 148-185. CrossRef. MathSciNet. Zentralblatt für Mathematik.
    • (1998) J. Differential Equations , vol.148 , Issue.1 , pp. 148-185
    • Novo, S.1    Núñez, C.2    Obaya, R.3
  • 15
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans
    • Zentralblatt für Mathematik
    • V. Oseledets, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197-231. Zentralblatt für Mathematik.
    • (1968) Moscow Math. Soc. , vol.19 , pp. 197-231
    • Oseledets, V.1
  • 17
    • 0001624408 scopus 로고
    • Existence of dichotomies and invariant splittings for linear differential systems. I
    • MathSciNet. Zentralblatt für Mathematik
    • R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I, J. Differential Equations 15 (1974), 429-458. MathSciNet. Zentralblatt für Mathematik.
    • (1974) J. Differential Equations , vol.15 , pp. 429-458
    • Sacker, R.J.1    Sell, G.R.2
  • 18
    • 49349126301 scopus 로고
    • A spectral theory for linear differential systems
    • MathSciNet. Zentralblatt für Mathematik
    • R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), no. 3, 320-358. MathSciNet. Zentralblatt für Mathematik.
    • (1978) J. Differential Equations , vol.27 , Issue.3 , pp. 320-358
    • Sacker, R.J.1    Sell, G.R.2
  • 19
    • 0031530247 scopus 로고    scopus 로고
    • The random attractor of the stochastic Lorenz system
    • CrossRef. MathSciNet. Zentralblatt für Mathematik
    • B. Schmalfuß, The random attractor of the stochastic Lorenz system, Z. Angew. Math. Phys. 48 (1997), no. 6, 951-975. CrossRef. MathSciNet. Zentralblatt für Mathematik.
    • (1997) Z. Angew. Math. Phys. , vol.48 , Issue.6 , pp. 951-975
    • Schmalfuß, B.1
  • 20
    • 84968520241 scopus 로고
    • Isolated invariant sets for flows on vector bundles
    • MathSciNet. Zentralblatt für Mathematik
    • J. F. Seigrade, Isolated invariant sets for flows on vector bundles, Trans. Amer. Math. Soc. 203 (1975), 359-390. MathSciNet. Zentralblatt für Mathematik.
    • (1975) Trans. Amer. Math. Soc. , vol.203 , pp. 359-390
    • Seigrade, J.F.1
  • 22
    • 0038399438 scopus 로고
    • A linear-quadratic problem of optimization and the frequency theorem for periodic systems. I
    • MathSciNet. Zentralblatt für Mathematik
    • V. A. Yakubovich, A linear-quadratic problem of optimization and the frequency theorem for periodic systems. I, Siberian Math. J. 27 (1986), no. 4, 614-630. MathSciNet. Zentralblatt für Mathematik.
    • (1986) Siberian Math. J. , vol.27 , Issue.4 , pp. 614-630
    • Yakubovich, V.A.1
  • 23
    • 0024085076 scopus 로고
    • Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part
    • CrossRef. MathSciNet. Zentralblatt für Mathematik
    • V. A. Yakubovich, Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part, Systems Control Lett. 11 (1988), no. 3, 221-228. CrossRef. MathSciNet. Zentralblatt für Mathematik.
    • (1988) Systems Control Lett. , vol.11 , Issue.3 , pp. 221-228
    • Yakubovich, V.A.1
  • 24
    • 0037723534 scopus 로고
    • A linear-quadratic problem of optimization and the frequency theorem for periodic systems. II
    • MathSciNet. Zentralblatt für Mathematik
    • V. A. Yakubovich, A linear-quadratic problem of optimization and the frequency theorem for periodic systems. II, Siberian Math. J. 31 (1990), no. 6, 1027-1039. MathSciNet. Zentralblatt für Mathematik.
    • (1990) Siberian Math. J. , vol.31 , Issue.6 , pp. 1027-1039
    • Yakubovich, V.A.1
  • 25
    • 0010013852 scopus 로고
    • Nonoscillation of linear periodic Hamiltonian equations and related problems
    • (Russian). MathSciNet. Zentralblatt für Mathematik
    • V. A. Yakubovich, Nonoscillation of linear periodic Hamiltonian equations and related problems, Algebra i Analiz 3 (1992), no. 5, 1165-1188 (Russian). MathSciNet. Zentralblatt für Mathematik.
    • (1992) Algebra I Analiz , vol.3 , Issue.5 , pp. 1165-1188
    • Yakubovich, V.A.1


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