Error State Convergence on Master–Slave Generalized Uncertain Neural Networks Using Robust Nonlinear $H_{\infty}$ Control Theory

Abstract

This paper addresses the convergence analysis on the guaranteed robust $H_{\infty }$ control for master–slave generalized uncertain neural networks (GUNNs). Synchronization problems are raised up due to the existence of the disturbance loading and parameter uncertainties. In order to cope with the encountered robustness issues, a dual geometric sequence division-dependent augmented Lyapunov–Krasovskii functional is newly constructed, which contains state variable-based integral forms with unfixed intervals. Meanwhile, the convex combination technique is employed to deal with not only the parameter uncertainties but also the derivative of delay $\dot {\tau } (t)$ . To ensure the GUNNs to be globally asymptotically stable with the guaranteed $H_{\infty }$ performance in the case of disturbance and parameters uncertainties, a controller is designed using the liner matrix inequalities technique. Numerical examples show that, in the sense of the prescribed $H_{\infty}$ performance, this proposed work achieves expected results on the error synchronization system.