Finite-time boundary control for delay reaction–diffusion systems

Abstract

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.