Discretization of Positive Control Systems—Symmetry Point of View

Positivity of a linear control system is interpreted as a symmetry with respect to transformations preserving the nonnegative cone of the state space. We study systems on arbitrary time scales and compare positivity criteria for different time scales. This allows us to establish conditions under which Euler discretization of a continuous-time positive system gives rise to a positive system on a discrete time scale. Then we study positive reachability and accessibility of positive systems on various time scales and show invariance of these properties with respect to Euler discretization.