Observer Design for a Class of Transport-Reaction Systems: a Direct Lyapunov Approach

The paper considers the observer design problem for a class of scalar distributed transport-reaction systems with boundary measurements, mixed Dirichlet-Neumann boundary conditions, linear (diffusive-convective) transport and nonlinear conically bounded source. A direct Lyapunov method is developed for the exponential stability analysis of the observation error. The Lyapunov functional is chosen with a constant kernel for the small values of the so-called Peclet number (i.e. the quotient of diffusion to convection time) and with a spatial-dependent kernel for high Peclet numbers. The derived Lyapunov-based stability conditions correspond to the ones based on the frequency-domain analysis. A numerical example illustrates the efficiency of the method.