Stabilization of Diffusion Equations under Sampled-Data Spatially Averaged Measurements

We develop distributed sampled-data control for parabolic systems governed by 1-d semilinear diffusion-convection equations. We suggest a sampled-data controller design, where the sampling intervals in time and in space are bounded. The network of N stationary sensing devices provide spatially averaged state measurements over the sampling spatial intervals. Our sampled-data static output feedback enters the equation through N shape functions (which are localized in the space) multiplied by the corresponding state measurements. Sufficient conditions for the exponential stability of the closed-loop system are derived via direct Lyapunov-Krasovskii method in terms of Linear Matrix Inequalities (LMIs). By solving these LMIs, upper bounds on the sampling intervals that preserve the exponential stability can be found.