Boundary Output Feedback for Fixed-time Stabilization of Distributed Parameter Systems With Time and Space Dependent Reactivity

The problem of boundary output feedback for fixed-time stabilization of parabolic distributed parameter systems with space and time dependent reactivity is considered by utilizing the backstepping method. An observer is constructed by applying the time-varying observer gain and boundary measurements, where the gain is unbounded as time approaches the terminal time. However, the fixed-time stability of error system is guaranteed by comparing the time growth rate of the observer gain with the decay rate of target error system state. Then, an observer-based output feedback boundary controller is established to achieve the fixed-time stabilization of the closed-loop system by combining the fixed-time stabilizing state feedback boundary controller and the fixed-time observer based on separation principle. Finally, a numerical simulation is shown to illustrate the effectiveness of the theoretical results.