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To extend the existing results of differential systems of integer order, we have considered a class of Caputo fractional linear differential systems with multiple delays. By applying the multinomial theorem for nonpermutable matrices without a commutativity assumption on the matrix coefficients, the representations of exact solutions for the studied systems were obtained. The results show that Hyers-Ulam stability in finite time holds for this class of systems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

For a class of unstable stochastic differential equations (SDEs)with jumps, the problem of stabilization with linear time-delay feedback controller is studied. Such an equation will have a unique solution, provided that its coefficients satisfy polynomial growth condition and Khasminskii type condition. By constructing integral Lyapunov functional, the coefficient matrix and time delay of the controller are determined. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Using the idea of step method, we discassed the existence and uniqueness of solutions of fractional neutral stochastic delay differential equations in the interval [0,τ],[τ,2τ],…,[（n-1）τ,nτ]. Combining Picard iterative method and integral operator theory, we proved that the solutions of fractional neutral stochastic delay differential equations are in existence and unique. The conclusions in existing literature are generalized and improved. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Donghua University (Natural Science Edition) is the property of Journal of Donghua University (Natural Science) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Donghua University (Natural Science Edition) is the property of Journal of Donghua University (Natural Science) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A class of nonlinear stochastic integro-differential dynamical systems were discussed, the necessary and sufficient conditions for the mean-square asymptotic stability of the zero solution to the system were given by means of the Banach fixed point method, and a mean-square asymptotic stability theorem for neutral Volterra stochastic integro-differential dynamical systems with multiple delays was established. Unlike the previous research methods, according to the characteristics of each time delay of the stochastic dynamical system with multiple time delays, the operators were constructed through introduction of the corresponding functions, and then the stability of the system was studied with the Banach fixed point method. The conclusion improves and develops the results of several related research papers to a certain extent. In addition, the results obtained supplement and extend those of the fixed point method in study of the stability of zero solutions to nonlinear neutral variable-delay Volterra stochastic integro-differential dynamical systems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The stabilization problem of a class of nonlinear stochastic delay differential equations driven by G? Brownain motion(G?SDDEs) was studied. Firstly,a delay feedback control was designed in the drift term of an unstable nonlinear G?SDDE, and the controlled system was therefore obtained. Then, with the Lyapunov technique,sufficient conditions for the asymptotical stability of the controlled system were given. Finally,two examples were presented to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The convergence of numerical solutions for Milstein Neutral Stochastic Delay Differential Equations with nonlinear coefficients is studied. A truncated Milstein numerical scheme is constructed for neutral stochastic delay differential equations with highly nonlinear coefficients by combining the truncation idea with the Milstein numerical scheme. Under the local Lipschitz condition and Khasminskii condition, it is proved that the truncated Milstein numerical solution Lp converges strongly to the exact solution for a neutral stochastic delay differential equation. The correctness of the conclusion is verified by numerical simulation for a specific neutral stochastic delay differential equation. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Guangdong University of Technology is the property of Journal of Guangdong University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The fuzzy H∞ controller design problem was studied for steam valve opening of multi-machine power systems which consisting of turbo-generators with mixed time-varying delays. The mixed time-varying delays include the interval retarded-type discrete delay， the neutral-type discrete delay and the time-varying distributed delays. Fuzzy models were established， and the controllers of the systems were designed. Linear matrix inequalities (LMIs)-based H∞ stability conditions were derived. Moreover， the results were expanded to different conditions of time-delay， including H∞ stability condition with the fast time-varying distributed delays (i.e. the derivatives of distributed delay is larger than 1). Therefore， the obtained results are new and less conservative. Finally， simulation results for the steam value opening of three-machine infinite bus systems were provided to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Aiming at the ecological system of the food chain predator-prey diffusion problem, a non-autonomous food chain diffusive predator prey model with discrete delay and distributed delay is discussed, obtaining the sufficient conditions of persistence and globally asymptotically stability of model by using comparison theorem and Lia-punov functional. [ABSTRACT FROM AUTHOR]

The delay estimation and compensation are key problems in real-time substructure testing because the delay of servo-hydraulic loading system may induce failure due to experimental instability. After analyzing the shortcomings. of the two other methods for estimating delay. the paper establishes an approximate relationship between displacements and system delay according to Taylor series firstly, and then proposes a real-time approach to delay estimation 'based on fading memory recursive Least-Square algorithm. Simulation results of delay estimation indicate that the approach converges rapidly and accurately, and is able to effectively track time-varying delay even though random measurement errors and amplitude errors are taken into account. A numerical example of real-time substructure testing with delay compensation shows that the accuracy and the convergence speed of the delay estimation method and the effect of delay compensation are rather satisfactory. The approach may be superior for real-time substructure testing to the two other methods. [ABSTRACT FROM AUTHOR]

A nonautonomous Lotka-Volterra predator-prey dispersal system with continuous and infinite time delays is considered. Firstly, by using comparison theorem and delay differential equation basic theory, the uniform permanence of the system under some appropriate conditions is proved. Secondly, by constructing suitable Lyapunov functional, the appropriate conditions for globally asymptotical stability of the system are obtained. Lastly, according to some results in the references, the system which has at least a positive periodic solution under the conditions for permanence is obtained. These results are basically an extension of the known results for nonautonomous Lotka-Volterra system, which enriches ecological meanings in models. [ABSTRACT FROM AUTHOR]

Since there exists non-Gaussian impulsive noise in real environment, a-stable distribution is taken as the noise model. And under this assumption, the problem of multi-source time delay estimation in passive systems is studied. Considering the effect of a-stable distributed noises for the classical second order statistics, combining fractional lower order statistics theory and chirp Z transformation (CZT), a novel multi-source time delay estimation method in impulsive noise environment is proposed. Simulations show that the proposed method is a high resolution method suited for a-stable distributed noises condition and its performance is better than that of the common method named covariation method. [ABSTRACT FROM AUTHOR]