Stabilization of nonautonomous linear parabolic-like equations: Oblique projections versus Riccati feedbacks

Abstract

An oblique projections based feedback stabilizability result in the literature is extended to a larger class of reaction-convection terms. A discussion is presented including a comparison between explicit oblique projections based feedback controls and Riccati based feedback controls. Advantages and limitations of each type of feedback are addressed as well as their finite-elements implementation. Results of numerical simulations are presented comparing their stabilizing performances for the case of time-periodic dynamics. Estimates are presented on the convergence rate of a proposed iterative algorithm to compute the time-periodic Riccati feedback.