Positive stabilization of a pure diffusion system

Abstract

This paper provides a complete analytical study of the positive stabilization, positive state estimation, and observer-based positive stabilization problems for a generic boundary control diffusion system with point observation. In particular, optimal design problems are solved analytically, and an original strategy for observer-based feedback stabilization is proposed. The three problems are also investigated for an arbitrary-order spatial discretization of the nominal PDE system enabling numerical implementation together with rigorous comparisons with the nominal solutions. In both the continuous and discretized settings, explicit and readily implementable solutions are derived.