Robust point control for a class of fractional-order reaction–diffusion systems via non-collocated point measurement

Abstract In this paper, stabilization problem of a class of anomalous reaction diffusion systems described by fractional-order reaction–diffusion equations (FRDEs) is studied via robust point control using non-collocated point measurement. To get over the difficulty created by non-collocated point measurement, an Luenberger-type FPDE state observer is established firstly. And then, observer-based output feedback controllers are designed for three cases: the number of controllers is less than and great than or equals to that of the observers’. By utilizing Lyapunov direct method, sufficient conditions of Mittag-Leffler (M-L) stability for FRDEs are derived in the form of linear matrix inequalities (LMIs), and the robustness analysis of the controllers to the reaction coefficient and diffusion coefficient of the system is given. Finally, numerical simulation shows the feasibility and validity of the proposed control method.