Invariance Properties in the Dynamics of Positive Linear Systems

The paper explores the dynamics of asymptotically stable positive linear systems, with arbitrary initial conditions and constant input signals. We study both discrete- and continuous-time cases. We prove the existence of time-dependent invariant sets, defined in terms of Holder p-norms, with 1 les p les infin. Our results allow refining the qualitative analysis of positive linear systems. The investigated invariance properties are not generally valid for asymptotically stable linear systems, in the absence of the positivity condition