Abstract
This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlinearity of a quadratic type on the basis of the Lyapunov’s direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.
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References
Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.
Barbashin, E. A. and Tabuyeva, V. A.: Dynamical Systems with the Cylinder Phase Space, Nauka, Moscow, 1969 (in Russian).
Barmish, B. R. and Hollot, C. V.: Counter-Example to a Recent Result on the Stability of Interval Matrices by S. Bialas, Int. J. Contr. 39 (5) (1984), pp. 1103–1104.
Bialas, S.: A Necessary and Sufficient Condition for Stability of Interval Matrices, Int. J. Contr. 37 (4) (1983), pp. 717–722.
Demidovich, B. P.: Lectures on Mathematical Theory of Stability, Nauka, Moscow, 1967 (in Russian).
Gantmacher, F. R.: The Theory of Matrices, Chelsea Publishing Company, New York, 1959.
Karl, W. C., Greschak, J. P., and Verghese, G. C.: Comments on “A Necessary and Sufficient Condition for Stability of Interval Matrices”, Int. J. Contr. 39 (4) (1984), pp. 849–851.
Kharitonov, V. L.: About an Asymptotic Stability of the Equilibrium Position of Linear Differential Equations Systems Family, Differential Equations 14 (11) (1978), pp. 2086–2088 (in Russian).
Kreinovich, V., Lakeyev, A., Rohn, J., and Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations, Kluwer Academic Publishers, Dordrecht, 1997.
Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.
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Ivlev, R.S., Sokolova, S.P. Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity. Reliable Comput 13, 283–291 (2007). https://doi.org/10.1007/s11155-006-9029-y
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DOI: https://doi.org/10.1007/s11155-006-9029-y