The notion of ranking was initiated into control theory by Glad a few yearsago. In this paper we mainly discuss one kind of rankings and study its invarianceproperties. This kind of rankings is closely related to the structure algorithm. The relationsbetween invariants of this kind of rankings and the invariants given by other studies, e.g.the invertibility indices of a system and so on, are examined. As applications of rankings,we deal with some well-known problems in "ranking technique". In this paper we mainlyintroduce a new method rather than solve new problems.
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