Sampled-Data Fractional Sliding Mode Observer Design for Nonlinear Perturbed Fractional Reaction Diffusion Neural Networks with Delay

This work studies an extension of sampled-data sliding mode observer (SMO) design for two cases of coupled nonlinear fractional reaction diffusion neural networks (FRDNNs) under time-varying delays and disturbances by sliding mode strategy. The first issue is with boundary input disturbances (BIDs). Another issue is with external distributed disturbances (EDDs). It is assumed that sensors provide spatial point measurements (SPMs), and a limited number of sensors are allocated in a spatial interval. Under SPMs, the design of sampled-data fractional sliding mode observer (SDFSMO) with robustness against BIDs or uncertain EDDs is explored, which ensures the error systems' asymptotic stability. Then, by using the fractional Lyapunov method, the sufficient conditions for desired performance are obtained. Conservatism is decreased via utilizing characteristics of sliding mode algorithm and nonlinear generalized Lipschitz continuity. Fractional numerical examples are stated to test the theoretical result.