Oblique projection output-based feedback exponential stabilization of nonautonomous parabolic equations

Abstract

A new output injection operator and a new feedback control operator are proposed to estimate and stabilize the state of linear nonautonomous parabolic equations. The proposed operators are time-independent and involve appropriately constructed oblique projections. Firstly, it is shown the estimating property of the dynamical Luenberger observer and the stabilizing property of the feedback controller. Then, it is shown the stability of the observer-controller coupled system, where the control input is dynamically constructed from the measured output. The numbers of actuators and sensors are finite. Finally, results of simulations are presented showing the stability of the closed-loop observer-controller coupled system.