Bounds on the size of minimal nonnegative realizations for discrete-time LTI systems

Abstract

Nonnegative linear time-invariant (LTI) state-space models are characterized by the property that their state variables and outputs remain nonnegative whenever the initial state and the inputs are nonnegative. Necessary and sufficient conditions for the existence of a nonnegative state-space realization of a given discrete-time (DT) impulse response were obtained recently. In this letter, we look at minimal nonnegative realizations of DT impulse responses and develop bounds on the number of state variables that are necessary.