On the absence of limit cycles in a class of state-space digital filters which contains minimum noise realizations

This paper presents a theorem for the absence of limit cycles in a class of state-space digital filters. Such a class contains minimum noise realizations of any order as a special case, that is, it is proved that the transition matrix A of minimum noise realizations of any order satisfies
I - A^{t}A \geq 0
, and thus the realizations are free of limit cycles.