Boundary Mittag-Leffler stabilization of fractional reaction-diffusion cellular neural networks

Abstract

Mittag-Leffler stabilization is studied for fractional reaction-diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a state-dependent boundary controller is designed when system states are available. By employing the spatial integral functional method and some inequalities, a criterion ensuring Mittag-Leffler stability of FRDCNNs is presented. Then, when the information of system states is not fully accessible, an observer is presented to estimate the system states based on boundary output and an observer-based boundary controller is provided aiming to stabilize the considered FRDCNNs. Furthermore, a robust observer-based boundary controller is proposed to ensure the Mittag-Leffler stability for FRDCNNs with uncertainties. Examples are given to illustrate the effectiveness of obtained theoretical results.

Keywords: Boundary control; Cellular neural networks; Fractional reaction–diffusion systems; Mittag-Leffler stability; Observer; Robust stability.