定常输出反馈任置极点的新结果*

A New Result for Pole Assignment Using Output Feedback

中文摘要

      本文指出，几乎所有满足如下不等式：r-1≥n-m-Σvij+t≥tμ的完全系统，都可以任意近似任置全部极点。这里n、r、m分别是系统的状态、输入、输出变量个数。{vi, i∈r}是(A, B)Kronecker指标，{vij, j∈t}是其子集。μ是(C, A)可观测指标。此条件式可概括以前的许多结果，如状态反馈(m=n, μ=1), m+r-1≥n的输出反馈等。文中有算例说明此条件式有效，并有反例指出了Kimura1977年的一个错误。本文是Kimura的结果上的修正和进一步推广。

英文摘要

      This paper says that arbitrary pole assignment is possible for almost all complete systems if r-1≥n-m-Σvij+t≥tμ. Here n, r, m is the number of states, of input, of output, respectively; {vi, i∈r} is the kronecker indice set of (A, B), {vij, j∈t}?{vi, i∈r}; μ is the observability index of (C, A); t is a natural number. This condition formula includes many results given before. For the case of t=1, Kimura 1977 had some other condition and algorithm. About it we gave a counter example. This paper is the amendment and extension from Kimura 1977 result.