Backstepping for coupled parabolic systems with spatially-varying coefficients

This contribution considers the extension of the backstepping method to coupled diffusion-convection-reaction systems with spatially-varying coefficients. The related kernel equations are derived for an exponentially stable target system with prescribed convergence rate. For the solution of the kernel equations the successive approximation is extended from the scalar to the considered multivariable case. Thereby, distinct and equal diffusion coefficients are taken into account in order to provide a general view of the backstepping control for coupled parabolic systems. The results of the paper are illustrated for a non- isothermal tubular reactor, that is described by two coupled semi-linear parabolic PDEs.