State–feedback stabilization of multi-input compartmental systems

In this paper we address the positive (state–feedback) stabilization of multi-input compartmental systems, i.e. the design of a state–feedback matrix that preserves the compartmental property of the resulting feedback system, while achieving stability. We first provide necessary and sufficient conditions for the positive stabilizability of compartmental systems whose state matrix is irreducible. Then we address the case when the state matrix is reducible, identify two sufficient conditions for the problem solution, and then extend them to a general algorithm that allows to verify when the problem is solvable and to produce a solution.