Finite-time local piecewise control for parabolic PDEs with ODE output feedback

This paper is devoted to the finite-time local piecewise control for parabolic partial differential equations (PDEs) by using dynamic output feedback control strategy, where the controller is designed as an ordinary differential equation (ODE). This makes the closed-loop system PDE-ODE coupled, which is employed to accurately describe the dynamics of the PDE system. According to the constructed PDE-ODE coupled model, a local piecewise dynamic feedback control law is first proposed. Sufficient conditions on finite-time stabilisation of the parabolic PDE-ODE coupled system by the suggested feedback controller are then developed in the sense of both complete spatial measurement and incomplete spatial measurement of the observed output of the PDE system, respectively. Finally, the issues regarding the finite-time stabilisation of the closed-loop system is converted into the feasibility of matrix inequalities, and some simulation studies are provided to verify the effectiveness of the proposed results.