A new guaranteed cost control for asymptotic stabilization of neural network with mixed time-varying delays via feedback control

Chalida Phanlert, Thongchai Botmart, Wajaree Weera, Patarawadee Prasertsang

Abstract

A new guaranteed cost control for asymptotic stability of the neural network with mixed time-varying delays and feedback control is studied. The considered mixed time-delays are both discrete and distributed time-varying delays. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov-Krasovskii functional includes double  integral term and triple integral term, utilizing Writinger-based integral inequality, extended reciprocally convex inequality and Jensen integral inequality, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Furthermore, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.