Static Output-Feedback Controller Synthesis for Linear MIMO Positive Delay Systems

Abstract

The static output-feedback controller synthesis problem is investigated in this paper for linear MIMO positive delay systems. The objective is to construct a static output-feedback controller such that the closed-loop system is positive, asymptotically stable, and the L₁-gain from the exogenous input to the regulated output is minimized. For the MIMO positive systems without delay, the necessary and sufficient condition for the existence of the controller is derived. Meanwhile, the new sufficient condition for the design of the controller of the MIMO positive systems with delay has been given. The condition in this paper breaks the limitations of existing methods in the literature where, for example, the state-space equation has a specific form, etc. Furthermore, the control gain can be easily obtained by linear programming (LP) approach. Several numerical experiments are carried out to illustrate the proposed results.