Logarithmically Completely Monotonic Rational Functions

TL;DR

This paper characterizes logarithmically completely monotonic rational functions, expanding the class of externally positive systems and enabling more efficient control design with less conservative conditions.

Contribution

It proposes new, less conservative conditions for rational functions to be LCM, facilitating improved control system design and pole-placement methods.

Findings

Conditions for rational functions to be LCM are less conservative.

Enlarges the class of externally positive linear systems.

Develops an efficient pole-placement procedure for monotonic tracking.

Abstract

This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising 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.