Optimal guaranteed cost synchronization of coupled neural networks with Markovian jump and mode-dependent mixed time-delay

This paper is concerned with the optimal guaranteed cost synchronization problem for a class of coupled neural networks with Markovian jump parameters and mode‐dependent mixed time‐delay. The coupled neural networks contained N‐identical delayed neural nodes and M switch modes from one mode to another according to a Markovian chaining with known transition probability. All the coupled networks' parameters covering the coupled matrix and discrete and distributed time‐delay also depend on the Markovian jump mode. The associated optimal guaranteed cost function is a quadratic function; the activation function is supposed to satisfy sector‐bounded condition. By employing a new Lyapunov–Krasovskii functional and some analytic skills, the sufficiency conditions of guaranteed cost synchronization are derived to ensure that coupling neural network is asymptotically synchronized for related cost function in mean square. The exported sufficient condition is closely contacted with the distributed time‐delay, the mode transition probability, the discrete‐time delay, and the coupled structure of networks. The achieved conditions are given in the light of LMI that can be usefully solved by using the semi‐definite program scheme. Moreover, an LMI‐based approach to export the guaranteed cost synchronization controller is formulated to minimize the optimal guaranteed cost for closed‐loop dynamical networks. Numerical simulations are developed to further display the efficiency of the achieved theoretical results