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

TL;DR

This paper compares oblique projection-based and Riccati feedback controls for stabilizing nonautonomous linear parabolic-like equations, extending existing results to broader reaction-convection terms and analyzing their numerical implementation and performance.

Contribution

It extends stabilization results to a larger class of equations and provides a detailed comparison between oblique projection and Riccati feedback methods, including numerical aspects.

Findings

Riccati feedback can be computed iteratively for periodic systems.

Both feedback methods are effective but have distinct advantages and limitations.

Numerical simulations compare their stabilization performance in time-periodic dynamics.

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 base 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. It is shown that the solution of the periodic Riccati based feedback can be computed iteratively.