Delayed Fuzzy Control of a 1-D Reaction-Diffusion Equation Using Sampled-in-Space Sensing and Actuation

This paper considers delayed fuzzy control of one-dimensional (1-D) reaction-diffusion equation under distributed in-domain point actuation and measurements. The delay may be uncertain, but bounded by a known upper bound. We propose an observer-based controller that employs the averaged values of the observer. Sufficient conditions ensuring exponential stability of the closed-loop system are established in terms of linear matrix inequalities by using the Lyapunov–Krasovskii method and the descriptor method. A numerical example demonstrates the efficiency of the results.