Abstract
By using Lyapunov functions, we obtain, for the first time, necessary and sufficient conditions for the exponential stability of some nonlinear systems of differential and difference equations.
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REFERENCES
L. T. Grujic, “Stability analysis of large-scale systems with stable and unstable subsystems,” Int. J. Contr., 2, 453–463 (1974).
S. K. Persidskii, “On the investigation of stability of solutions of nonlinear systems of differential equations,” Prikl. Mat. Mekh., 34, 219–226 (1970).
E. A. Barbashin, Lyapunov Functions [in Russian], Nauka, Moscow (1970).
S. K. Persidskii, “Application of homogeneous polynomials as Lyapunov functions,” Dinam. Sist., Issue 16, 15–21 (2000).
S. K. Persidskii, “Absolute stability of nonlinear systems of finite-difference equations,” in: Differential Equations and Their Applications [in Russian], Kazakh State University, Alma-Ata (1979), pp. 114–116.
K. P. Persidskii, “On the second Lyapunov method,” Izv. Akad. Nauk Kazakh. SSR, Ser. Mat., No. 42, Issue 1, 48–53 (1947).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 131–136, January, 2005.
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Persidskii, S.K. On the Exponential Stability of Some Nonlinear Systems. Ukr Math J 57, 157–164 (2005). https://doi.org/10.1007/s11253-005-0178-7
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DOI: https://doi.org/10.1007/s11253-005-0178-7