Linear positive control systems on time scales. Controllability

TL;DR

This paper develops a unified theory for positive linear control systems on arbitrary time scales, providing new controllability conditions that extend known results from continuous and discrete systems.

Contribution

It introduces a necessary and sufficient condition for positivity and controllability of linear systems on general time scales, using a modified Gram matrix approach.

Findings

Unified framework for continuous and discrete positive systems

Necessary and sufficient controllability conditions on time scales

Characterization of positive reachable sets

Abstract

Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear system on a time scale to be positive is presented. Properties of positive reachable sets are investigated and characterizations of various controllability properties are presented. A modified Gram matrix of the system is used to state necessary and sufficient condition of positive reachability of a positive system on an arbitrary time scale.