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Sufficient conditions for stability of periodic linear impulsive delay systems. (English. Russian original) Zbl 1406.93242

Autom. Remote Control 79, No. 11, 1989-2004 (2018); translation from Avtom. Telemekh. 2018, No. 11, 47-66 (2018).
Summary: For a linear periodic system with impulsive action and delay, new approaches to the study of stability are proposed on the basis of the methods of spectral theory of linear operators, direct Lyapunov method, and N. G. Chetaev method for construction of the Lyapunov functions for the periodic linear systems, as well as the perturbation method for construction of the Lyapunov functions. These methods underlie sufficient conditions for asymptotic stability of the linear periodic systems with impulsive action and delay. We gave some illustrative examples of studying stability of such systems under different assumptions about the dynamic properties of the continuous and discrete components of the impulsive system.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C05 Linear systems in control theory
34A37 Ordinary differential equations with impulses
93D20 Asymptotic stability in control theory
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