不确定二维多项式族的稳定性检验集合

不确定二维多项式族,包括多胞形二维多项式族,区间二维多项式族,钻石形二维多项式族,其鲁棒稳定性可由其棱边多项式的稳定性确定.如果二维多项式族的不确定参数较多,被检验棱边多项式的数目可能出现所谓组合爆炸问题.为解决这一问题,提出一检验集合,该集合根据棱边二维多项式的凸方向来构造,仅对属于该检验集合棱边二维多项式进行稳定性检验,从而大大地减少被检验的棱边二维多项式数目.给出一例来说明这种新方法的可行性.

STABILITY TEST SET FOR UNCERTAIN TWO-DIMENSIONAL POLYNOMIAL FAMILY

Robust stability of uncertain two-dimensional (2-D) polynomial family, including polytopes of 2-D polynomials, interval 2-D polynomial family, diamonds of 2-D polynomial family, depends on that of the edge polynomials of the families. If the number of uncertain parameters of the 2-D polynomial family is large, there may exist the problem of the so called "combination exploration" for the number of the edges of 2-D polynomials to be tested. To solve the problem, a test set has been developed, which is based on the convex direction of edge polynomials, and the number of edge polynomials can be greatly reduced. An example has been given to demonstrate the applicability of the new approach.