Extended Luenberger-type observer for a class of semilinear time fractional diffusion systems

This paper is concerned with the design of an extended Luenberger-type observer to deal with the observation problem for a class of semilinear time fractional diffusion systems, which are usually used to well describe those sub-diffusion processes, such as water moving through grounds, or proteins diffusing across cell membranes etc. Mittag-Leffler stability for both the linearized and semilinear observer error systems are explored by using a backstepping-based technique. Moreover, a simulation example is provided to confirm the effectiveness of our results.