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Reachability and minimum energy control of positive discrete-time linear systems with multiple delays in state and control

Kaczorek T., Busłowicz M.

Pomiary Automatyka Kontrola

2007

R. 53, nr 10

40-44

A notion of positive linear discrete-time systems with multiple delays in state and control is introduced. The necessary and sufficient conditions for positivity, reachability and minimum energy control are given. Considerations are illustrated by example.

W pracy podano warunki, przy spełnieniu których liniowy dyskretny układ z wieloma opóźnieniami zmiennych stanu i sterowania jest układem dodatnim. Podano też warunki konieczne i wystarczające osiągalności oraz sterowania z minimalną energią. Rozważania zilustrowano przykładem.

Cohort-type models and their reachability and controllability properties.

James D.J.G., Rumchev V.G.

Systems Science

2000

Vol. 26, nr 2

43-54

Cohort-type models have a wealth of structure and are important in many fields of application. Being a sub-class of linear positive systems, such a model structure belongs to this class of constrained linear systems which are defined on cones and not on linear spaces. As a consequence much of the theory developed for linear systems is not directly applicable. Whilst the dynamics of cohort-type models. Are well understood their reachability and controllability properties have received little attention in the literature. Using a graph-theoretic characterisation the paper examines these fundamental properties and includes application to some specific models.