Geodesic
The convergence of the method of constructing the Lyapunov matrix for~time-delay systems
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2015), pp. 150-159

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In this paper the problem of stability analysis of delay system with periodic coefficients was studied. Exponential stability was analyzed by the method of Lyapunov–Krasovskii functional. Necessity of use of the explicit Lyapunov matrix was resolved by proposing a numerical method for construction of the Lyapunov matrix for any period and delay in the system: for the simple case of commensurate dimensions of delay and period, and for the complex case of any dimensions. High efficiency of used method was estimated by comparison with well-known Lyapunov matrices for special induced stationary systems. Bibliogr. 9.
Keywords: delay systems, stability, Lyapunov matrix. 
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K. A. Slupko. The convergence of the method of constructing the Lyapunov matrix for~time-delay systems. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2015), pp. 150-159. http://geodesic.mathdoc.fr/item/VSPUI_2015_1_a13/