Exponential stability of continuous-time and discrete-time neural networks with saturated impulses

This paper investigates the exponential stability of neural networks (NNs) with saturated impulses that have different impulsive effects (i.e., stabilizing and destabilizing impulses) in both continuous-time and discrete- time situations. For the purpose of generating discrete-time analogues that maintain the dynamic characteristics of the considered systems, the semi-discretization approach is first applied to the continuous-time NNs with saturated impulses. Secondly, for the prescribed initial condition, the bounds of states of the system at the impulsive instants were estimated by using the quadratic Lyapunov function method and the average impulsive interval (AII) technique, which ensure that the saturation nonlinearities at the impulsive instants can be handled by the sector nonlinear model approach (SNMA) and the polyhedral representation approach (PRA), respectively. Furthermore, less conservative criteria for the exponential stability of the saturated impulsive continuous neural networks and their discrete-time analogues have been derived. Thirdly, an algorithm based on linear matrix inequalities (LMIs) has been presented to achieve an enlarged estimation of the region of attraction (ROA) under stabilizing impulses. This algorithm addresses the pertinent optimization problems and provides the design of an impulsive controller. Finally, the validity of the obtained results is verified through numerical examples and simulations, and the theoretical results are applied to the exponential synchronization of chaotic neural networks under saturated impulsive control.