Explicit exponential stabilization of nonautonomous linear parabolic-like systems by a finite number of internal actuators

摘要: An explicit feedback controller is proposed for stabilization of linear parabolic equations, with a time-dependent reaction–convection operator. The range the finite-dimensional, and typically modeled by indicator functions small subdomains. Its dimension depends polynomially on suitable norm A sufficient condition stabilizability given, which involves asymptotic behavior eigenvalues (time-independent) diffusion operator, nonorthogonal projection onto controller’s along infinite-dimensional (higher-modes) eigenspace. To construct feedback, essential step consists in computing projection. Numerical simulations are presented, 1D 2D, showing practicability its response to measurement errors, where actuators subsets.