Finite-time boundary control for delay reaction-diffusion systems

This paper considers finite-time stabilization and H∞ performance for delay reaction-diffusion systems by boundary control. First, a full-domain controller is designed and sufficient conditions are obtained to achieve finite-time stability using finite-time stability lemma and Wirtinger's inequality method. Then a boundary controller furnished with sufficient conditions to achieve finite-time stability is presented. When taking into consideration external noise on a delay reaction-diffusion system, finite horizon H∞ boundary control with a criterion that guarantees the H∞ performance of delay reaction-diffusion systems is proposed. How to handle Neumann boundary conditions and mixed boundary conditions are discussed. Numerical simulations are carried out to verify the effectiveness of our theoretical results.