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2 International Journal of Applied Mathematics and Computer Science

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Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

Raja R., Sakthivel R., Anthoni S. M., Kim H.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 1

127-135

The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as theMatlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

Controllability of nonlinear impulsive Ito type stochastic systems

Sakthivel R.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 4

589-595

In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.