混合不确定系统鲁棒稳定性检验的数值方法

Numerical Approach to Robust Stability Test of Mixed Uncertain Systems

混合不确定系统的鲁棒稳定性问题可以转化为一有理函数簇边界的H∞范数检验问题.为了减小计算复杂性,对一类线性部分仿射取决于变化参数的混合不确定系统,探讨了其数值求解方法.结果表明在固定的频率上边界对象的象是复平面上的一圆弧.对此文中获得了一个新的最大圆弧范数计算公式并诱导出一个可在有限频率范围内进行边界检验的算法.

The robust stability analysis of mixed uncertain systems can be completed by testing the H ∞ norm of edges of an uncertain rational function. To reduce the computational complexity, a numerical approach is proposed for a class of mixed uncertain systems whose coefficients affinely dependent on system parameters. It is shown that the image of an edge rational function at a fixed frequency is an arc in s plane. Further, a new formula to compute the maximal norm of the arc is developed. Based on these results an edge test algorithm in a finite frequency range is induced by which the computational burden can be greatly reduced.