The authors present explicit expressions for two different cascade factorizations of any detectable system which is not necessarily left invertible and which is not necessarily strictly proper. The first is a well-known minimum phase/all-pass factorization by which G(s) is written as G/sub m/(s)V(s), where G/sub m/(s) is left invertible and of minimum phase, while V(s) is a stable right invertible all-pass transfer function matrix which has all unstable invariant zeros of G(s) as its invariant zeros. The second is a generalized cascade factorization by which G(s) is written as G/sub M/(s)U(s), where G/sub M/(s) is left invertible and of minimum-phase with its invariant zeros at desired locations in the open left-half s-plane, while U(s) is a stable right invertible system which has all awkward invariant zeros, including the unstable invariant zeros of G(s), as its invariant zeros, and is asymptotically all-pass.
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机译：作者给出了任何可检测系统的两个不同级联分解的显式表达式，这些系统不一定是不可逆的，并且不一定严格正确。第一个是众所周知的最小相位/全通分解，通过该最小化，G（s）可以写为G / sub m /（s）V（s），其中G / sub m /（s）保持可逆，且G / sub m /（s）保持可逆。最小相位，而V（s）是一个稳定的右可逆全通传递函数矩阵，其中G（s）的所有不稳定不变零均是其不变零。第二个是广义级联分解，通过该级联分解，G（s）可以写为G / sub M /（s）U（s），其中G / sub M /（s）保持可逆，并且其最小相位为零。 U（s）是一个稳定的右可逆系统，它具有所有尴尬的不变零，其中包括G（s）的不稳定不变零，作为其不变零，并且是渐近的全部通过。
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