Guaranteed Cost Boundary Control for Uncertain Markov Jump Delay Reaction‐Diffusion Neural Networks

ABSTRACT The paper investigates the guaranteed cost boundary control (GCBC) for uncertain Markov jump reaction‐diffusion neural networks (UMJRDNNs) with constant delay and time‐varying delay. Firstly, for UMJRDNNs with constant delay, a sufficient criterion is established to achieve the GCBC with a completely known transition rate matrix (TRM) employing the Lyapunov functional method and inequality techniques. An upper bound of the given cost function is confirmed by the obtained sufficient criterion. Secondly, the uncertain TRM is investigated, and a sufficient criterion is also presented to achieve the guaranteed cost under the designed boundary control for UMJRDNNs with time‐varying delay. Moreover, an upper bound can be obtained for the cost function. Finally, two numerical examples are presented to verify the validity of the theoretical results.