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• W2735981021 abstract "In this paper, a general class of nonlinear dynamical systems described by retarded differential equations with discontinuous right-hand sides is considered. Under the extended Filippov-framework, we investigate some basic stability problems for retarded differential inclusions (RDI) with given initial conditions by using the generalized Lyapunov-Razumikhin method. Comparing with the previous work, the main results given in this paper show that the Lyapunov-Razumikhin function is allowed to have a indefinite or positive definite derivative for almost everywhere along the solution trajectories of RDI. However, in most of the existing literature, the derivative (if it exists) of Lyapunov-Razumikhin function is required to be negative or semi-negative definite for almost everywhere. In addition, the Lyapunov-Razumikhin function in this paper is allowed to be non-smooth. To deal with the stability, we also drop the specific condition that the Lyapunov-Razumikhin function should have an infinitesimal upper limit. Finally, we apply the proposed Razumikhin techniques to handle the stability or stabilization control of discontinuous time-delayed neural networks. Meanwhile, we present two examples to demonstrate the effectiveness of the developed method." @default.
• W2735981021 created "2017-07-21" @default.
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• W2735981021 date "2017-01-01" @default.
• W2735981021 modified "2023-09-23" @default.
• W2735981021 title "Generalized Lyapunov-Razumikhin method for retarded differential inclusions: Applications to discontinuous neural networks" @default.
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• W2735981021 doi "https://doi.org/10.3934/dcdsb.2017181" @default.
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