Delay-partitioning-based reachable set estimation of Markovian jump neural networks with time-varying delay

Abstract

The objective of this paper is to estimate the reachable set for a class of delayed neural networks (NNs) subject to Markovian jump parameters and bounded disturbance. First, by virtue of delay-partitioning method, the time-varying delay is divided into some delay components. With suitably constructing Lyapunov–Krasovskii functionals (LKFs), a less conservative delay-dependent condition of finding an ellipsoid-like set to contain all state trajectories that start from the origin is derived in terms of linear matrix inequalities (LMIs). Then the integrally free-matrix-based inequality approach together with the extended reciprocally convex technique is employed to further reduce the conservatism on characterizing bounds of some integral terms. Thanks to a group of free-connection weighting matrices, the proposed reachable set estimation approach is extended to the case that transition probabilities are partially known. Finally, numerical simulations indicate that the derived results are effective and less conservative.