菱形对象族的顶点镇定结果

Extreme Point Results for Robust Stabilization of Diamond Plants

本文研究了菱形对象族的鲁棒镇定问题．当控制器取为分子，分母为仅有奇次项的或仅有偶次项的多项式的真有理分式时，证明了该控制器鲁棒镇定菱形对象族的充分必要条件为该控制器同时镇定三十二个顶点对象．当上述控制器的分子，分母限于正负交错系数的仅有奇次项的或仅有偶次项的多项式时，该控制器鲁棒镇定菱形对象族所需同时镇定的顶点对象最多为十六个，所得结果与对象族的阶次无关．

The paper studies the stabilization of diamond plants with the compensator which is proper and its numerator and denominator are even or odd polynomials. It is proved that the necessary and sufficient condition for the compensator to robustly stabilize the diamond plants is that it simultaneously stabilizes thirty-two vertex plants. If the numerator and the denominator of the above compensator are confined to the even or odd polynomials with their coefficients positively and negatively interlaced,then for the compensator to robustly stabilize the diamond plants,it only needs to simultaneously stabilize at most sixteen vertex plants. The results obtained are independent of the order of the plants.