This paper studies the variation diminishing property of k-positive linear time-invariant (LTI) systems, which diminish number sign changes (variation) from input to output, if is at most k?1. We characterize this for discrete-time Toeplitz and Hankel operators finite-dimensional causal systems. Our main result that these have a dominant approximation in form series or parallel interconnections...

Positive systems play an important role in and control theory have found many applications multiagent systems, neural networks, biology, more. map the nonnegative orthant to itself (and also nonpositive itself). In other words, they set of vectors with zero sign variations itself. this article, discrete-time linear that up k - 1 are introduced. For special case = these reduce positive systems. ...