Positive realization of discrete-time systems by geometric approach

The positive realization problem treated in this paper is that of finding a linear state realization from the given transfer function, such that all the coefficients of the realization are nonnegative. The specific problems treated here are realizability conditions and the way of getting positive realizations. These problems are discussed in detail through convex cone analysis and downsampling technique. It is shown that the problem of positive realizability is reduced to a set of the problems of positive realizability corresponding to the downsampled impulse responses.