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Stability of Systems with Nonlinearities

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Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

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Abstract

In Chap. 5 stability of the zero solution and positive equilibrium points for nonlinear systems is studied. In particular, differential equations with nonlinearities in deterministic and stochastic parts are considered, differential equation with fractional nonlinearity. It is shown that investigation of stability in probability for nonlinear systems with the level of nonlinearity higher than one can be reduced to investigation of asymptotic mean square stability of the linear part of the considered nonlinear system. The obtained results are illustrated by 18 figures.

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Authors and Affiliations

  1. Department of Higher Mathematics, Donetsk State University of Management, Donetsk, Ukraine

    Leonid Shaikhet

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  1. Leonid Shaikhet
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Shaikhet, L. (2013). Stability of Systems with Nonlinearities. In: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00101-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-00101-2_5

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00100-5

  • Online ISBN: 978-3-319-00101-2

  • eBook Packages: EngineeringEngineering (R0)

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