Filter design of delayed static neural networks with Markovian jumping parameters

This paper considers the H∞H∞ filtering problem of static neural networks with Markovian jumping parameters and time-varying delay. A mode and delay dependent approach is presented to deal with it. By constructing a stochastic Lyapunov functional with triple-integral terms and employing a recently proposed integral inequality, a design criterion is derived under which the resulting filtering error system is stochastically stable with a guaranteed H∞H∞ performance. Based on it, the proper gain matrices and optimal H∞H∞ performance index can be efficiently obtained via solving a convex optimization problem subject to some linear matrix inequalities. An advantage of this approach is that most of the Lyapunov matrices are distinct with respect to system mode and thus the choice of these matrices becomes much flexible. Finally, an example is provided to illustrate the application and effectiveness of the developed result.