Minimal order realizations for a class of positive linear systems

The positive realization problem for linear systems is to find, for a given transfer function, all possible realizations with a state space of minimal dimension such that the resulting system is a positive system. In this paper, discrete-time positive linear systems having the nonnegative orthant reachable from the origin in a finite time interval with nonnegative inputs, are considered and the solution of the positive realization problem for this class of systems is given.