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Titlebook: Lyapunov Functionals and Stability of Stochastic Difference Equations; Leonid Shaikhet Book 2011 Springer-Verlag London Limited 2011 Contr

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書目名稱Lyapunov Functionals and Stability of Stochastic Difference Equations
編輯Leonid Shaikhet
視頻videohttp://file.papertrans.cn/590/589172/589172.mp4
概述Detailed description of Lyapunov functional construction will allow researchers to analyse stability results for hereditary systems more easily.Profuse analytical and numerical examples help to explai
圖書封面Titlebook: Lyapunov Functionals and Stability of Stochastic Difference Equations;  Leonid Shaikhet Book 2011 Springer-Verlag London Limited 2011 Contr
描述Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using a Lyapunov functional. .Lyapunov Functionals and Stability of Stochastic Difference Equations describes a general method of Lyapunov functional construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues. .The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functional construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical systems including inverted pendulum control, study of epidemic dev
出版日期Book 2011
關(guān)鍵詞Control Theory; Lyapunov Functionals Construction; Numerical Analysis; Stability Theory; Stochastic Diff
版次1
doihttps://doi.org/10.1007/978-0-85729-685-6
isbn_softcover978-1-4471-7166-9
isbn_ebook978-0-85729-685-6
copyrightSpringer-Verlag London Limited 2011
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Linear Equations with Nonstationary Coefficients,ons with nonstationary coefficients. Three different ways of the construction of Lyapunov functionals are shown, which allows one to get different types of sufficient conditions for asymptotic mean square stability of the trivial solution of the considered equation with nonstationary coefficients. S
地板
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Some Peculiarities of the Method,method allows us to get not sufficient stability conditions only, but the necessary and sufficient stability conditions for the trivial solution of stochastic linear difference equation too. It is shown that different ways of the estimation of the Lyapunov functional increment allow us to get differ
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Nonlinear Systems, nonlinear systems and for different types of stability. It is shown that, using the procedure of the construction of Lyapunov functionals, investigation of stability in probability of a nonlinear stochastic difference equation with order of nonlinearity higher than 1 can be reduced to the investiga
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發(fā)表于 2025-3-22 19:54:39 | 只看該作者
Volterra Equations of Second Type, of the construction of Lyapunov functionals and also by the resolvent representation of a solution. In particular sufficient conditions for .-summability, .≥1, for the solution of a stochastic difference second kind Volterra equation are obtained, and linear equations with constant and variable coe
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Leonid Shaikhetnd war-avoidance that is clearly supportive of what has for the sake of brevity somewhat unattractively been described as the ‘circumscribed idealist hypothesis’. While in no sense wishing to deny that in many contexts —arguably the most important ones in terms of the broad sweep of world events — l
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