Robust Stabilization of Delayed Neural Networks: Dissipativity-Learning Approach

This paper examines the robust stabilization problem of continuous-time delayed neural networks via the dissipativity-learning approach. A new learning algorithm is established to guarantee the asymptotic stability as well as the <inline-formula> <tex-math notation="LaTeX">$(Q,S,R)$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\alpha$ </tex-math></inline-formula>-dissipativity of the considered neural networks. The developed result encompasses some existing results, such as <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> and passivity performances, in a unified framework. With the introduction of a Lyapunov–Krasovskii functional together with the Legendre polynomial, a novel delay-dependent linear matrix inequality (LMI) condition and a learning algorithm for robust stabilization are presented. Demonstrative examples are given to show the usefulness of the established learning algorithm.