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This article focuses on the design of proportional‐derivative (PD) controllers for positive linear systems in the continuous‐time domain, which is a well‐known open problem in positive systems theory. The main objective is to design a PD controller subject to interval gain variations, which simultaneously preserves the closed‐loop system stability and positivity. The provided results fill the literature gap by considering both the PD controller structure and positivity. Although various feedback control strategies of positive systems have been developed recently, the work provides, for the first time, a systematic and tractable framework for finding nonfragile PD controller gains for positive stabilization. Finally, the theory and algorithm performance are evaluated and illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

• The PD controller design problem of positive discrete-time systems with constant delay is tackled in this work. • A systematic formulation is proposed to design non-fragile PD controllers for such kind of systems. • Based on the necessary and sufficient conditions derived, two tractable linear-programming-based and semi-definite-programming-based algorithms are developed for calculating the solution. This paper addresses the issue of proportional-derivative (PD) controllers design for positive linear systems in the discrete-time domain, which still remains a challenging problem in positive systems theory. The specific aim is to design a PD controller for a system with constant time delay, which simultaneously ensures closed-loop system stability and preserves positivity. Moreover, additive gain variation of the controller is considered in the synthesis process. Systematic formulation and tractable algorithms are developed to find the PD controller gains for positive stabilization. The performance of such methods is validated by numerical examples. [ABSTRACT FROM AUTHOR]