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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]

Summary: This paper addresses the problem of switching control for systems subject to external disturbances that vary over multiple frequency ranges. Specifically, two different scenarios of disturbance injection are considered; namely, the disturbance may switch between different prescribed frequency ranges, subject to an average dwell time setting, or the disturbance may reside within one of the frequency ranges. To address these scenarios, a disturbance‐triggered control scheme is developed that divides the entire frequency range into low‐, mid‐, and high‐frequency ranges. This scheme ensures closed‐loop stability under average dwell time frequency‐range switching and achieves H∞$$ {H}_{\infty } $$ performance when operated under individual frequency ranges. Synthesis conditions in matrix inequalities are derived to characterize the switching control, and an iterative algorithm is proposed for finding a desired set of controller gains. Finally, two examples are presented to illustrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]