中文摘要：

研究了气动弹性系统的不确定性建模和鲁棒颤振分析问题。将结构的不确定性考虑为参数形式，非定常气动力的不确定性考虑为参数和未建模动态两种形式，建立了不确定系统的线性分式变换模型。分别使用基于Carathedory—Fejer插值定理和Nevanlinna—Pick插值定理的模型集检验方法进行了模型确认，在时间域和频率域中对模型集的有效性进行了验证，确定了不确定性的幅值。对于模型确认得到的不确定气动弹性系统，使用μ分析方法进行了鲁棒颤振分析。计算中，飞行速度是作为给定参数而不再是作为摄动变量，由此得到的鲁棒稳定性边界是匹配点解。仿真数值结果给出了鲁棒颤振速度，表明了方法的有效性。

英文摘要：

The problems of uncertainty modeling and robust flutter analysis of aeroelastic system are investigated in this paper. The parametric uncertainty is considered to denote the uncertainty in structure, and both parametric form and unmodeled dynamics are used to represent the influences and mechanism of uncertainty in unsteady aerodynamic forces. The Linear Frac- tional Transformation representation of the uncertain aeroelastic system is formulated to perform model validation and robust flutter analysis. The model validation methods based on Carathedory-Fejer interpolation theorem and Nevanlinna-Piek interpolation theorem are used to verify the validity of the model set, both in time-domain and frequency-domain and the magnitudes of the uncertainties are determined. Then, for the uncertain aeroelastic system with the obtained uncertainty magni- tudes, the robust flutter analysis based on structured singular value theory is performed to predict the robust stability boundary. Since the flight speed is used as a given parameter instead of perturbation variable, the obtained robust stability boundary is match point solution. Numerical results are presented and the predicted robust flutter speeds demonstrate the validity of the developed method.