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Browsing by Author "Slynko, Vitalii"

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    Article
    Exponential Stability in the L P-Norm of Nonlinear Coupled Hyperbolic Spatially Inhomogeneous Systems
    (Elsevier Science inc, 2024) Slynko, Vitalii; Tunc, Osman; Atamas, Ivan
    We study exponential stability of equilibrium in the L (P) -norm (1 < P <= infinity, P not equal 2) of nonlinear 1D systems of hyperbolic equations. A method of construction of Lyapunov functions based on the W. Magnus representation of fundamental solutions of ordinary differential equation (ODE) linear systems is proposed. Sufficient conditions for exponential L (P) -stability (1 < P < infinity, P not equal 2) are obtained and sufficient conditions for exponential L (infinity) -stability are derived by passing to the limit. The obtained results are compared with the well-known results.
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    Article
    Stability of Abstract Linear Switched Impulsive Differential Equations
    (Pergamon-elsevier Science Ltd, 2019) Slynko, Vitalii; Tunc, Cemil
    Linear impulsive switched differential equations in Hilbert space are studied. We propose a new method of stability investigation, which is based in constructing an equivalent impulsive system without switching. Using operator-valued and scalar Lyapunov functions, sufficient conditions for Lyapunov stability of linear switched impulsive equations in a Banach space are established. The examples of studies of this class of equations with periodic switching are given. (C) 2019 Elsevier Ltd. All rights reserved.