Boundary observers for coupled diffusion–reaction systems with prescribed convergence rate

Abstract

Following recent results on the boundary stabilization of coupled first-order hyperbolic equations by means of integral transformations, here a new result is presented for the problem of state estimation of coupled linear reaction–diffusion PDEs with Neumann boundary conditions from boundary measurements. For this purpose, an observer is constructed with a prescribed convergence rate. The stability of the estimation error system is derived by mapping the estimation error system to a stable target system using a pair of integral transformations. Our method is applicable as well to the dual problem of boundary stabilization of coupled linear reaction–diffusion PDEs. A numerical scheme, based on power series approximations of the kernels is formulated, taking into account the fact that the kernels are only piecewise differentiable.