94 research outputs found
LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion
The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ξ©), ItΓ΄ formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays
Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays
published_or_final_versio
Π‘ΠΈΡΡΠ΅ΠΌΠΈ Π΄ΠΈΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»Π½ΠΈ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΈ Π½Π΅Π²ΡΠΎΠ½Π½ΠΈ ΠΌΡΠ΅ΠΆΠΈ ΡΡΡ Π·Π°ΠΊΡΡΠ½Π΅Π½ΠΈΡ ΠΈ ΠΈΠΌΠΏΡΠ»ΡΠΈ
Department of Mathematics & Statistics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman ΠΈ ΠΠΠ-ΠΠΠ, 16.06.2014 Π³., ΠΏΡΠΈΡΡΠΆΠ΄Π°Π½Π΅ Π½Π° Π½Π°ΡΡΠ½Π° ΡΡΠ΅ΠΏΠ΅Π½ "Π΄ΠΎΠΊΡΠΎΡ Π½Π° Π½Π°ΡΠΊΠΈΡΠ΅" Π½Π° ΠΠ°Π»Π΅ΡΠΈΠΉ ΠΠΎΠ²Π°ΡΠ΅Π² ΠΏΠΎ Π½Π°ΡΡΠ½Π° ΡΠΏΠ΅ΡΠΈΠ°Π»Π½ΠΎΡΡ 01.01.13. ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠ°Π½Π΅ ΠΈ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Π½Π° ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΠΊΠ°ΡΠ°. [Covachev Valery Hristov; ΠΠΎΠ²Π°ΡΠ΅Π² ΠΠ°Π»Π΅ΡΠΈΠΉ Π₯ΡΠΈΡΡΠΎΠ²
Stochastic Processes with Applications
Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included
Fixed Points and Exponential Stability for Impulsive Time-Delays BAM Neural Networks via LMI Approach and Contraction Mapping Principle
The fixed point technique has been employed in the stability analysis of time-delays bidirectional associative memory (BAM) neural networks with impulse. By formulating a contraction mapping in a product space, a new LMI-based exponential stability criterion was derived. Lately, fixed point methods have educed various good results inspiring this work, but those criteria cannot be programmed by a computer. In this paper, LMI conditions of the obtained result can be applicable to computer Matlab LMI toolbox which meets the need of the large-scale calculation in real engineering. Moreover, a numerical example and a comparable table are presented to illustrate the effectiveness of the proposed methods
Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function
This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results
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