Octavian PĂSTRĂVANU, Mihaela-Hanako MATCOVSCHI, Mihail VOICU
New Results in the State-Space Analysis of Positive Linear Systems

Abstract.
The paper provides new results for the state-space analysis of positive linear systems, with arbitrary initial conditions and constant input signals. These results explore the invariance properties in the dynamics of asymptotically stable positive linear systems. We prove there exist families of time-dependent sets, defined in terms of Hölder p-norms, 1 ≤ p ≤ ∞, that are invariant with respect to the system trajectories. We study both discrete- and continuous-time dynamics. Our work refines the qualitative analysis of positive linear systems, in the sense that the invariance properties investigated by us are not generally valid for asymptotically stable linear systems, if the positivity condition is missing.