A new result on reachable set estimation for Markovian jump neural networks with time-varying delays

This paper is concerned with the problem of reachable set estimation (RSE) for a class of delayed Markovian jump neural networks with periodically time-varying delay. First, by augmenting the state-related vectors in the double integral term and combining with zero inequalities, more cross-term information is captured. According to periodicity and monotonicity, the time-varying delay is divided into monotonically decreasing and increasing intervals. Then, by constructing delay-product terms in each interval, a novel Lyapuov-Krasovskii functional is derived, which contributes to the reduction of conservatism, and thus a refined allowable set of the delay is obtained. Finally, two improved RSE criteria that consider complete and incomplete transition probabilities are obtained, by which smaller bounded sets can be found with less conservatism. In the simulation section, numerical examples are given to demonstrate the superiority of the method.