The solution of a transcendental problem and its applications in simultaneous stabilization problems
The solution of a transcendental problem and its applications in simultaneous stabilization problems
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DOI：
10.1109/9.159568
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发表时间：
1992-09
影响因子：
6.8
通讯作者：
K. Wei
中科院分区：
文献类型：
--
作者：
K. Wei
给出了系统论中一个特殊超越问题的完全解。这个超越问题的解释之一是下面的同时稳定问题：在什么条件下可以同时稳定两个线性植物由一个单一的补偿器没有真实的极点在封闭的右半平面的复？这些条件是完全通用的，因此也包括不稳定的非最小相位植物。它表明，通过这样的限制补偿器的两个给定的植物的同时稳定性仅取决于两个植物的真实的零点的位置和他们的差植物在封闭的右半复平面。对于两个植物满足稳定性条件，一个计算的设计过程，构建一个所需的补偿器提供和说明。给出了三个被控对象同时镇定的一个计算可检验的必要条件。>
A complete solution for a special transcendental problem in system theory is given. One of the interpretations of this transcendental problem is the following simultaneous stabilization problem: under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane? These conditions are completely general and therefore encompass unstable non-minimum-phase plants as well. It is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane. For two plants satisfying the stabilizability conditions, a computational design procedure for constructing a desired compensator is provided and illustrated. A computationally checkable necessary condition for simultaneous stabilization of three plants is also given. >