Transcendental and interpolation methods in simultaneous stabilization and simultaneous partial pole placement problems
Transcendental and interpolation methods in simultaneous stabilization and simultaneous partial pole placement problems
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DOI：
10.1137/0324066
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发表时间：
1986-11
影响因子：
2.2
通讯作者：
B. Ghosh
中科院分区：
文献类型：
--
作者：
B. Ghosh
在本文中，我们调查的存在性的补偿器，同时使一个给定的r-元组的多输入多输出p \times m$线性动力系统内部稳定。特别是我们parametrize一组同时稳定的r-元组的植物，并表明，提供$r \leqq \max（m，p）$，上述集合是半代数和密集的空间$\Sigma $的r-元组的植物。此外，我们还考虑了经典极点配置和镇定问题的推广，并研究了部分极点配置问题。因此，我们考虑一个合适的拓扑结构，并获得了一个必要条件和充分条件的一般部分极点配置问题。令人惊讶的是，同时稳定的三重$m \倍m$植物，一般选择的问题，示出相当于部分极点放置一个单一的$m \倍m$植物由一个稳定的最小相位补偿器的问题。另一方面，问题的同时...
In this paper, we investigate the existence of a compensator which simultaneously renders a given r-tuple of multiinput multioutput $p \times m$ linear dynamical systems internally stable. In particular we parametrize a set of simultaneously stabilizable r-tuples of plants and show that provided $r \leqq \max (m,p)$, the above set is semialgebraic and dense in the space $\Sigma $ of r-tuples of plants. Furthermore, we also consider an extension of the classical pole placement and stabilization problems and investigate the simultaneous partial pole placement problem. Consequently, we consider a suitable topology in and obtain a necessary condition and a sufficient condition for the generic partial pole placement problem. Surprisingly enough, the problem of simultaneously stabilizing a triplet of $m \times m$ plants, chosen generically, is shown equivalent to the problem of partially pole placing a single $m \times m$ plant by a stable minimum phase compensator. On the other hand the problem of simultaneous...