Logarithmically completely monotonic rational functions

This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterizing externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking. Conditions are proposed to ensure a rational function is LCM, a result that enables the known space of linear continuous-time externally positive systems to be enlarged and an efficient and optimal pole-placement procedure for the monotonic tracking controller synthesis problem to be developed. The presented conditions are shown to be less conservative than existing approaches whilst being computationally tractable.& COPY; 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper examines the category of logarithmically completely monotonic (LCM) functions and their importance in characterizing externally positive linear systems. It proposes conditions for ensuring a rational function is LCM, which expands the space of linear continuous-time externally positive systems and allows for the development of an efficient and optimal pole-placement procedure for the monotonic tracking controller synthesis problem. These conditions are less conservative than existing approaches and computationally tractable.