Intermittent boundary control for fixed-time stability of reaction-diffusion systems

This work is a pilot effort to investigate the fixed-time stability (FxTS) of reaction-diffusion systems under aperiodically intermittent boundary control (AIBC). The average control rate and a new Lyapunov function are proposed to overcome the challenges of handling the FxTS of reaction-diffusion systems with AIBC. Moreover, the proposed method is applicable to the study of finite -time stability and exponential stability of reaction- diffusion systems under AIBC. Based on the Wirtinger's inequality and the Lyapunov method, a FxTS criterion for a reaction-diffusion system with AIBC is given. Finally, two examples are discussed along with the simulated results to verify the effectiveness of the proposed method.