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. |