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Positive state controllability of discrete linear time-invariant systems

Ouyadri Mourad, Laabissi Mohamed, Achhab Mohammed Elarbi

Acta Mechanica et Automatica

2024

Vol. 18, no. 1

110--118

Positive state controllability is the controllability of systems where the state is positive and the input remains in ℝn. Under some conditions, we established a relation between the reachability map of systems with only the positive state and the reachability map of a related positive system where the state and input are both positive. Using this connection, necessary and sufficient conditions are obtained for the positive state reachability of discrete linear time-invariant (LTI) systems, and then we deduced the positive state controllability. These conditions are evaluated over some numerical examples that support the theoretical results.

Positive output controllability of linear discrete–time invariant systems

Ouyadri Mourad, Laabissi Mohamed, Achhab Mohammed Elarbi

Control and Cybernetics

2021

Vol. 50, No. 4

521--539

This paper studies the output controllability of discrete linear time invariant systems (LTI) with non-negative input constraints. Some geometrical arguments and positive invariance concepts are used to derive the necessary and/or sufficient conditions for the positive output controllability of discrete LTI systems. The paper also provides several academic examples, which support the theoretical results.