Boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems

In this paper, the problem of boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems is studied. Firstly, the stability of the target system is analyzed. By using the backstepping method, the explicit kernel matrix function is obtained, and a new state feedback controller is designed to stabilize the original system. Then we consider two kinds of output measurements, that is, the non-collocated output and the collocated output. In the two cases, the corresponding observers and output feedback controllers are designed, respectively, to achieve the asymptotical stability of the studied system.