Static Output-Feedback Stabilization for MIMO LTI Positive Systems using LMI-based Iterative Algorithms

Abstract

This letter proposes two iterative algorithms for solving static output feedback stabilization problem for LTI multi-input multi-output systems. Contrary to the existing literature, in this letter, no restrictive assumption has been made on the state-space description of the open-loop plant for which a static output feedback controller is to be designed to synthesize a stable internally positive system in closed-loop. Algorithm 1 involves the cone complementarity linearization technique to overcome the underlying difficulties of BMI problem, whereas the success of Algorithm 2 depends on a scalar search associated with a positive definite matrix obtained as the stabilizing solution of a Riccati equation. Numerical examples show that, in some cases where the existing algorithms fail, the proposed algorithms can find a static output feedback stabilizing controller ensuring the positive system properties.