Control design for suppressing transversal patterns in reaction–(convection)–diffusion systems

The stabilization of planar stationary fronts solutions in a two-dimensional rectangular or cylinder domain, in which a diffusion–convection–reaction process occurs, is studied by reducing the original two-variable PDEs model to an approximate one-dimensional model that describes the behavior of the front line. We consider the control strategy based on sensors placed at the designed front line position and actuators that are spatially-uniform or space dependent. We present a systematic control design that determines the number of required sensors and actuators, their position and their form. The control used linear analysis of a lumped truncated model and concepts of finite and infinite zeros of linear multidimensional systems.