On the reachability in any fixed time for positive continuous-time linear systems

Christian Commault (1) , Mazen Alamir (2)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

This paper deals with the reachability of continuous-time linear positive systems. The reachability of such systems, which we will call here the strong reachability, amounts to the possibility of steering the state in any fixed time to any point of the positive orthant by using nonnegative control functions. The main result of this paper essentially says that the only strongly reachable positive systems are those made of decoupled scalar subsystems. Moreover, the strongly reachable set is also characterized.

Mots clés: Systèmes positifs; atteignabilité en temps quelconque

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Christian Commault, Mazen Alamir. On the reachability in any fixed time for positive continuous-time linear systems. Systems and Control Letters, 2007, 56 (6), pp.272-276. ⟨10.1016/j.sysconle.2006.10.021⟩. ⟨hal-00108502⟩