# LFT Modeling and Robust Stability Analysis of Missiles with Uncertain Parameters

• Hou, Zhen-Qian (Automation College, Northwestern Polytechnical University) ;
• Liang, Xiao-Geng (Automation College, Northwestern Polytechnical University) ;
• Wang, Wen-Zheng (China Aerodynamics Research & Development Center) ;
• Li, Rui (Xi'an Wuhua Juneng Blasting Equipment Co., Ltd.)
• Accepted : 2014.06.13
• Published : 2014.06.30

#### Abstract

The structured singular value (${\mu}$) analysis based method has many advantages for the robust stability analysis of missiles with uncertain parameters. Nevertheless, the present linear fractional transformation (LFT) modeling process, which is the basis of ${\mu}$ analysis, is complex, and not suitable for automatic implementation; on the other hand, ${\mu}$ analysis requires a large amount of computation, which is a burden for large-scale application. A constructive procedure, which is computationally more efficient, and which may lead to a lower order realization than existing algorithms, is proposed for LFT modeling. To reduce the calculation burden, an analysis method is developed, based on skew ${\mu}$. On this basis, calculation of the supremum of ${\mu}$ over a fixed frequency range converts into a single skew ${\mu}$ value calculation. Two algorithms are given, to calculate the upper and lower bounds of skew ${\mu}$, respectively. The validity of the proposed method is verified through robust stability analysis of a missile with real uncertain parameters.

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