Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays

This paper is concerned with the exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays. The parameters of the neural networks are subject to the switching from one mode to another according to a Markov chain. By constructing a novel Lyapunov-Krasovskii functional and developing a new convex combination technique, a new delay-dependent exponential stability condition is proposed, such that for all admissible delay bounds, the resulting estimation error system is mean-square exponentially stable with a prescribed noise attenuation level in the H∞ sense. It is also shown that the design of the desired state estimator is achieved by solving a set of linear matrix inequalities (LMIs). The obtained condition implicitly establishes the relations among the maximum delay bounds, H∞ noise attenuation level and the exponential decay rate of the estimation error system. Finally, a numerical example is given to show the effectiveness of the proposed result.