纯量反馈系统同时强镇定的充分条件

Sufficient Conditions for Strong Simultaneous Stabilization of Scalar Feedback Systems

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n+1个对象(同时镇定).两个以上对象的同时强镇定和三个以上对象的同时镇定是线性系统中一个急待解决的公开问题.文中所作的基本假定是所有的对象具有相同的简单不稳定零点,在此条件下给出了n个对象同时强镇定的一个充分条件.当仅有一个不稳定零点时,容易检验是否同时强镇定,否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的,就能判定n个对象同时强镇定.因此是一个易于检验的充分条件.文章同时给出了n个对象同时强镇定的算法,丰富了同时强镇定的充分条件.

As is well known, the existence of a single stable controller to stabilize a set of n SISO plants (strong simultaneous stabilization) is equivalent to a single controller, not necessarily stable, to stabilize n+1 plants (simultaneous stabilization). Strong simultaneous stabilization and simultaneous stabilization are two open questions in linear systems. Under the assumption that all the plants have the same simple unstable zeros, this paper give a sufficient condition for strong simultaneous stabilization. When there is only one unstable zero, it is easy to defermine whether the n plants can be strong simultaneous stabilizatoin; otherwise, in order to insure whether n SISO plants can be strong simultaneous stabilization, it is only necessary to determine the unstable zeros of the n plants, and to determine whether the corresponding matrix determined by the unstable zeros is positive definite. This paper also give a algorithm to determine the simultaneous stabilization controller, and enrich the sufficient conditions for strong simultaneous stabilization.