同时强镇定的一个充分条件

A sufficient condition for strong simultaneous stabilization

一个稳定的控制器可同时镇定n个对象(同时强镇定)等价于一个控制嚣(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亟待解决的公开问题.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.此条件仅需确定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.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条件和算法.

As is well known, a single stable controller which stabilizes n SISO plants (strong simultaneous stabilization) is equivalent to a single controller (not necessarily stable) which stabilizes n+1 plants (simultaneous stabilization). Strong simultaneous stabilization and simultaneous stabilization are two open problems that need to be solved urgently in linear systems. Under the assumption that all the plants have the same simple unstable zeros, this paper gives a sufficient condition for strong simultaneous stabilization. Under this condition, in order to insure n SISO plants to be strong simultaneous stabilization, it is only necessary to determine the unstable zeros of n plants, and to determine whether the corresponding matrix determined by the unstable zeros is positive definite. This paper also gives an algorithm to determine the simultaneous stabilization controller, and thus enriches the condition and algorithm for the strong simultaneous stabilization.