Some theoretical results based on passivity for linear time-invariant digital filters

In this paper, a suitable definition of passivity is chosen for linear and time-invariant digital filters, which are described only by state-space equations without any knowledge of their structures. The rational transfer function or transfer matrix of such a passive digital filter is so-called unitary-bounded. In general, the converse of this statement is not true. However, any digital filter possessing a unitary-bounded rational transfer function or transfer matrix is passive if it is minimal. Some further theoretical results based on this definition of passivity are also presented.