Producing Stable Periodic Solutions of Switched Impulsive Delayed Neural Networks Using a Matrix-Based Cubic Convex Combination Approach.

Abstract

This article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time-varying delays. First, tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks. Second, a sufficient criterion for the existence, uniqueness, and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse-delay-dependent Lyapunov-Krasovskii functional method. It is worth emphasizing that the addressed Lyapunov-Krasovskii functional covers both triple integral terms and novel quadruple integral terms, which makes the conservatism of the above criteria decrease. Even if the original neural network models are unstable or the impulsive effects are strong, the addressed neural network model can produce a globally exponentially stable periodic solution. These results here, which include boundedness, globally uniformly exponential convergence, and globally exponentially stability of the periodic solution, generalize and improve the earlier publications. Finally, two numerical examples and their computer simulations are given to show the effectiveness of theoretical results.