Optimal H∞ synchronization of general discrete-time delayed chaotic neural networks via dynamic output feedback

This paper deals with robust H_∞ synchronization of general discrete-time chaotic neural networks with external disturbance. This general discrete-time model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers not only several well-known discrete-time delayed neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs), but also Lur´e systems. Based on Lyapunov stability and H_∞ control theories, dynamic output feedback controllers are established to not only guarantee exponentially stable synchronization of both master and slave systems with time delays, but also reduce the effect of external disturbance to an H_∞-norm constraint. Furthermore, two classes of optimal controllers are presented, one minimizing the H_∞-norm bound, the other maximizing the exponential synchronization rate. The control design equations are shown to be a set of linear matrix inequality (LMI) standard problems which can be easily solved by various convex optimization algorithms to determine the optimal H_∞ control laws and the optimal exponential synchronization rates.