New Results on Global Exponential Convergence of Discontinuous HCNNs with Time-Varying Leakage Delays

This paper presents a class of high-order cellular neural networks (HCNNs) with mixed discontinuous activations and time-varying leakage delays. To deal with the discontinuous property, the framework of Filippov solution is invoked to solve the inexistence of the classical solutions. Then combining with the functional differential inclusions theory and inequality technique, some new verifiable algebraic criteria are given to ensure that all solutions of the proposed neural network converge exponentially to the zero vector. The results obtained in this paper not only extend earlier works on HCNNs to the discontinuous case but also complement the previous researches on discontinuous neural networks since the mixed discontinuous activations have never been touched. Consequently, the results we established are more generalized. Finally, the effectiveness of the obtained results are illustrated via numerical examples and simulations.