This paper concentrates on the study of robust stability of fractional order system with polynomial uncertainties. Polynomial uncertainties means that the coefficients of the fractional system are polynomial functions of the parameters, and the uncertain parameters vary in semialgebraic set. The roots of the fractional order characteristic function are assigned in the shifted half plane. Therefore, the fractional system can maintain certain robustness and time domain performance. In order to check the robust stability of fractional order polynomial system, alternative methods are presented by using Sum of Squares (SOS) programs. Since SOS programs can be all written as Linear Matrix Inequalities (LMI) feasibility tests, our proposed method embraces the advantages of LMI techniques. Numerical examples are presented to illustrate the proposed results.

本文重点研究具有多项式不确定性的分数阶系统的鲁棒稳定性。多项式不确定性意味着分数系统的系数是参数的多项式函数，并且不确定参数在半代数集中有所不同。分数阶特征函数的根在偏移的半平面中分配。因此，分数系统可以保持一定的鲁棒性和时域性能。为了检查分数阶多项式系统的鲁棒稳定性，使用平方和提出了替代方法。（SOS）程序。由于SOS程序都可以写为线性矩阵不等式（LMI）可行性测试，因此我们提出的方法具有LMI技术的优势。数值例子说明了所提出的结果。