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exponential estimates FOR STOCHASTIC DELAY EQUATIONS WITH NORM-BOUNDED UNCERTAINTIES

Journal of Systems Science & Complexity 2009年第2期22卷 324-332页

作者： Hongchu WANG Shigeng HU School of Mathematics Science South China Normal University Guangzhou 510631 China. Department of Mathematics Huazhong University of Science and Technology Wuhan 430074 China.

This paper presents the sufficient conditions for the exponential stability of linear or semi-linear stochastic delay equations with time-varying norm bounded parameter ***-tial estimates for the solutions are also obtained by using a modified Lyapunov-Krasovski *** conditions can be tested numerically using interior point algorithms.

关键词： exponential estimates time delay uncertainty.

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Synchronization and exponential estimates of Complex Networks with Mixed Time-varying Coupling Delays

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International Journal of Automation and computing 2009年第3期6卷 301-307页

作者： Yang Dai Yun-Ze Cai Xiao-Ming Xu Department of Automation Shanghai Jiao Tong University Shanghai 200240 PRC University of Shanghai for Science and Technology Shanghai 200093 PRC Shanghai Academy of Systems Science Shanghai 200093 PRC

exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities （LMIs）. A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed timevarying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

关键词： Complex networks synchronization exponential estimates neutral delay time-varying delay.

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Exit problems for nonlinear stochastic evolution equations on Hilbert spaces

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Science China Mathematics 2002年第10期45卷 1238-1254页

作者：梁宗霞 Department of Mathematical Sciences Tsinghua University Beijing China

This paper extends exit theorems of Da Prato and Zabczyk to nonconstant diffusion *** uses extensively general, exponential estimates due to Peszat.

关键词： exit time exponential estimates nonlinear stochastic evolution equations

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Variation of Constant Formulae for Time Invariant and Time Varying Caputo Fractional Delay Differential Systems

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Journal of Mathematical Research with Applications 2014年第5期34卷 549-560页

作者： Hai ZHANG Daiyong WU Department of Mathematics Anqing Normal University Department of Mathematics Southeast University

This paper studies the variation of constant formulae for linear Caputo fractional delay differential *** discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall’s integral *** variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform *** terms of the superposition principle of linear systems and fundamental solution matrix,we also establish the variation of constant formula for linear time varying fractional delay differential *** obtained results generalize the corresponding ones of integer-order delayed differential equations.

关键词： fractional delay differential systems variation formula exponential estimates Laplace transform Gronwall’s integral inequality.

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