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Linear positive control systems on time scales; controllability. (English) Zbl 1270.93015

Summary: 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.

MSC:

93B05 Controllability
93C05 Linear systems in control theory
15B48 Positive matrices and their generalizations; cones of matrices
93B03 Attainable sets, reachability
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