Discrete-Time $k$-Positive Linear Systems

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. Properties analyzed using tools from sign-regular matrices. particular, it is shown almost every solution such converges variations. It induce a dynamics k-dimensional parallelotopes.