Explicit expressions for cascade factorization of general nonminimum phase systems

Explicit expressions for two different cascade factorizations of any detectable left invertible nonminimum phase systems are given. The first one is a well known minimum phase/all-pass factorization by which all nonminimum phase zeros of a transfer function G(s) are collected into an all-pass factor V(s), and G(s) is written G/sub m(s)V/$ where G/sub m/s is considered as a minimum phase image of G(s). The second one is a new cascade factorization by which G(s) is rewritten as G/sub M/(s)U(s) where U(s) collects all 'awkward' zeros including all nonminimum phase zeros of G(s). Both G/sub m/(s) and G/sub M/(s) retain the given infinite zero structure of G(s). Further properties of G/sub m/(s), G/sub M/(s), and U(s) are discussed. These factorizations are useful in several applications including loop transfer recovery.<
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