Search

The robust stochastic convergence and stability in mean square are investigated for a class of uncertain neutral-type neural networks with both Markovian jump parameters and mixed delays. First, by employing the Lyapunov method and a generalized Halanay-type inequality for stochastic differential equations, a delay-dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a prespecified convergence rate. Next, by applying the Jensen integral inequality and a novel reciprocal convex lemma, a delay-dependent criterion is developed to achieve the globally robust stochastic stability in mean square. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of LMIs, which can be solved numerically by employing the standard MATLAB LMI toolbox package. Finally, two illustrated examples are given to show the effectiveness and less conservatism of the obtained results over some existing works. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The exponential stability problem is investigated for a class of uncertain stochastic neural networks with discrete and unbounded distributed time delays. Two types of uncertainty are considered: one is time-varying structured uncertainty, whereas the other is interval uncertainty. With the application of the Jensen integral inequality and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The global exponential stability is analyzed for a class of high-order Hopfield-type neural networks with time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-independent and delay-dependent sufficient conditions are presented for the global exponential stability of the equilibrium point of the considered neural networks. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. [ABSTRACT FROM AUTHOR]

An augmented Lyapunov-Krasovskii functional (LKF) approach is presented to derive sufficient conditions for the existence, uniqueness, and globally exponential stability of the equilibrium point of a class of cellular neural networks with time-varying delays. By dividing the variation interval of the time delay into several subintervals with equal length, a novel vector LKF is introduced and new conditions are obtained based on the homeomorphism mapping principle, free-weighting matrix method, and linear matrix inequality techniques. Since the criteria are involving derivative information of both state and delay, the obtained results are less conservative than some previous ones. Two examples are also given to show the effectiveness of the presented criteria.