Reachable set estimation for discrete-time Markovian jump neural networks with unified uncertain transition probability

Abstract

This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay. By allowing uncertainty in the transition probabilities, a framework unifies and enhances the generality and realism of these systems. To fully exploit the unified uncertain transition probabilities, an equivalent transformation technique is introduced as an alternative to traditional estimation methods, effectively utilizing the information of transition probabilities. Furthermore, a vector Wirtinger-based summation inequality is proposed, which captures more system information compared to existing ones. Building upon these components, a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities. A numerical example is illustrated to demonstrate the superiority of the approaches.