The servomechanism problem for SISO positive LTI systems

Abstract

In this paper, we study the servomechanism problem for positive LTI systems. In particular, we consider the robust servomechanism problem of nonnegative constant reference signals for stable SISO positive LTI systems with constant disturbances, for the case when the plant model of the system is not known. A positive LTI system is an LTI system with the imposed constraint that the state, output and/or input variables be nonnegative for all time. This type of constraint is quite natural to apply, since the property of nonnegativity occurs quite frequently in practical applications and in nature, e.g. in pharmacodynamic applications, infusion of vasoactive drugs, chemical systems. A special class of positive systems that is of significant importance and appears quite frequently in the literature is the class of compartmental systems; these systems are composed of a finite number of storage devices or reservoirs and model various gas, fluid, and solid exchange networks. Positive systems have been of great interest to numerous researchers over several decades. Interesting results obtained on positive systems span the topics of reachability and controllability, realization theory for positive systems, stability control, and control via pole-assignment. However, to date, there appears that no study has been carried out on the servomechanism problem for positive LTI systems; thus we focus our attention on this topic in the paper. Various applications of the results are applied to a number of positive system problems obtained from the literature. © 2008 Springer London.