On the reachability and controllability of positive linear time-invariant dynamic systems with internal and external incommensurate point delays

Abstract

This paper is devoted to the characterization of reachability and controllability properties of singular linear time-delay, time-invariant dynamic positive systems subject to constant known internal and external point delays. The research is performed on two different levels, namely, based on a general nonunique solution trajectory including discontinuities at points of the initialization time-interval and based on a particular solution with initial conditions in an appropriate subspace of the whole potential admissible set which avoids such discontinuities and guarantees uniqueness. In this second case, the positivity, reachability and controllability characterizations of the Weierstrass canonical state-space realization are also investigated. Copyright © 2010 Rocky Mountain Mathematics Consortium.