H_∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback control.

Abstract

This paper investigates the H_∞ master-slave synchronization problem for delayed impulsive implicit hybrid neural networks based on memory-state feedback control. By developing a more holistic stochastic impulse-time-dependent Lyapunov-Krasovskii functional and dealing with the nonlinear neuron activation function, the stochastic admissibility and prescribed H_∞ performance index for the synchronization error closed-loop system are achieved. In addition, the desired mode-dependent memory-state feedback synchronization controller is acquired in the form of linear matrix inequalities. The free-weighting matrix technique is adopted to remove the inherent limitation of time-varying delay derivative for the implicit delayed systems, and the derivative of time-varying delay is relaxed enough to be greater than 1. The simulation of genetic regulatory network in bio-economic system is given to verify validity of the derived results.