Mathematics, 2023 In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension of the classical asymptotical stability theorem in terms of a Lyapunov–Razumikhin function is ...
Natalya O. Sedova, Olga V. Druzhinina
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Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique [PDF]
Abstract and Applied Analysis, 2010 This paper develops some new Razumikhin-type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations.
Shiguo Peng, Liping Yang
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Razumikhin-type stability criteria for differential equations with delayed impulses [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2013 This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations.
Qing Wang, Quanxin Zhu
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Systems and Control Letters, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiyin Fei, Xuerong Mao
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Input-to-state stability for discrete time-delay systems via the Razumikhin technique
Systems and Control Letters, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bin Liu, David Hill
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Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique [PDF]
Statistics and Probability Letters, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiafeng Pan, Chunhai Kou, Xuerong Mao
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Discrete Razumikhin-type technique and stability of the Euler--Maruyama method to stochastic functional differential equations [PDF]
Discrete and Continuous Dynamical Systems, 2013 A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of
Fuke Wu, Xuerong Mao, Peter E Kloeden
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Numerical Algebra, Control and OptimizationThis paper generates the Razumikhin method to the stabilization problem of hybrid stochastic systems with intermittent discrete-state feedback control, where two main problems are settled: one is discrete-time state period, the other is intermittent control strategy.
Xuerong Mao
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Lyapunov-Razumikhin techniques for state-dependent delay differential equations [PDF]
Journal of Differential Equations, 2021 We present Lyapunov stability and asymptotic stability theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin methods. Our results apply to DDEs with multiple discrete state-dependent delays, which may be nonautonomous for the Lyapunov stability result, but autonomous (or ...
A.R. Humphries, F.M.G. Magpantay
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Estimates for solutions of homogeneous time-delay systems: comparison of Lyapunov–Krasovskii and Lyapunov–Razumikhin techniques [PDF]
International Journal of Control, 2021 In this contribution, the estimates for the response of time delay systems with nonlinear homogeneous right-hand side of degree strictly greater than one are constructed. The existing results obtained via the Lyapunov--Razumikhin approach are reminded.
Gerson Portilla +3 more
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