一类多项式族的鲁棒稳定性分析

Robust Stability Analysis for a Class of Polynomial Family

考虑摄动参数呈多项式映射关系的一类多项式族的鲁棒稳定性分析问题.基于线性矩阵不等式(Linear Matrix Inequality,LMI)方法,给出了这类多项式族的稳定判据,以及多项式族的最大鲁棒稳定域估计.由于非线性解析函数可用多项式任意逼近,故该方法也可用于具有一般非线性参数摄动的多项式族的鲁棒稳定性分析.最后,通过算例验证了该方法的可行性.

Robust stability analysis for a class of polynomial family with polynomial perturbation parameters is considered. Based on linear matrix inquality（LMI）, a stability criterion is presented for the class of polynomial family. Moreover, a method is also provided to estimate the maximal stability domain. Since an analytic function can be arbitrary approximated by a polynomial, the provided methods can be applied to robust stability analysis of polynomial family with general non-linear perturbation parameters. Finally, an illustrative example is given to show the feasibility of the methods in practice.