Robust Observer Design for Coupled Semilinear Time-Fractional Diffusion Systems with State-Dependent Coefficients

This paper concerns the problem of robust observer design for coupled semilinear time-fractional diffusion systems with state-dependent coefficients via pointwise in-domain measurements. Toward this aim, a pointwise measurement injection robust observer is proposed. We then discuss Mittag-Leffler stability of the resulting observer error system by using Kirchhoff transformation and fractional Lyapunov direct method. Our obtained results can offer some insights into the observer design theory of time-fractional diffusion systems and are hoped to be applied in real applications. An example is finally presented to illustrate the effectiveness of our theoretical results.