Observer based control for a class of coupled parabolic hyperbolic systems

This paper investigates the control problem for a class of highly nonlinear-coupled partial differential equations that describe radiative-conductive heat transfer systems. Thanks to the special structure of the obtained state system, using the Galerkin method for the semi-discretization of PDE and to the differential mean value theorem (DMVT), a new LMI condition is provided for the observer-based controller design. The observer and controller gain are computed simultaneously by solving linear matrix inequality (LMI), i.e a convex problem. Also we provide a reduced order observer based controller that assures global asymptotic stability.