$$H_{\infty }$$ H ∞ filter design for delayed static neural networks with Markovian switching and randomly occurred nonlinearity

Abstract

The paper is concerned with the problem of $$H_{\infty }$$ filter design for delayed static neural networks with Markovian switching and randomly occurred nonlinearity. The random phenomenon is described in terms of a Bernoulli stochastic variable. Based on the reciprocally convex approach, a lower bound lemma is proposed to handle the double- and triple-integral terms in the time derivative of the Lyapunov function. Finally, the optimal performance index is obtained via solving linear matrix inequalities(LMIs). The result is not only less conservative but the time derivative of the time delay can be greater than one. Numerical examples with simulation results are provided to illustrate the effectiveness of the developed results.