Manlika Rajchakit, Grienggrai Rajchakit
Department of Mathematics and Statistics
Maejo University
Chiangmai, 50290, THAILAND

Abstract. This paper studies the problem of guaranteed cost control for a class of Hopfield delayed neural networks. The time delay is a continuous function belonging to a given interval, but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functional combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control and new sufficient conditions for the existence of the guaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs).

Received: January 16, 2014

AMS Subject Classification: 92B05, 93D20, 37C75

Key Words and Phrases: Hopfield neural networks, guaranteed cost control, stabilization, interval time-varying delays, Lyapunov function, linear matrix inequalities

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