Positive quadratic stabilization of uncertain linear system

This paper considers the problem of positive quadratic stabilization of uncertain linear system by state feedback. First, we provide preliminary results on quadratic stabilization and formulate it in terms of LMI for a specific uncertainty structure imposed on the system. This step is accomplished by taking advantage of the Bounded Real Lemma (BRL). Next, we use the stability properties of the class of positive continuous-time system in order to formulate a constrained stabilization problem for general systems using state feedback. The Metzlerian stabilization can also be performed using LMI. Finally, we tie the LMI associated with quadratic stabilization and the LMI associated with Metzlerian stabilization to provide a complete solution to positive quadratic stabilization. We also outline the procedure of generalizing our approach for the delay case. A numerical example is included to support the theoretical results.