Boundary output feedback stabilization of state delayed reaction–diffusion PDEs

Abstract

This paper addresses the problem of output feedback stabilization of a class of 1-D reaction–diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition. The system output is selected as either a Dirichlet or Neumann boundary trace. The developed control design procedure does not aim to compensate, but rather to dominate the state delayed term. This is achieved by introducing an observer that only estimates a finite number of modes of the PDE while applying a suitable pole shifting-based procedure on a truncated model that captures the unstable part of the plant. We show that the reported output feedback control strategy always achieves, for an arbitrarily given value of the state delay, the exponential stabilization of the plant in H1-norm. A notable feature of the domination-based approach is that the tuning of the controller and observer gains, as well as the subsequent stability conditions, appears to be independent of the value of the state delay.