有结构摄动非线性系统的鲁棒绝对稳定性

ON ROBUST ABSOLUTE STABILITY OF NONLINEAR SYSTEMS WITH STRUCTURED PERTURBATIONS

考虑非线性闭环系统的鲁棒绝对稳定性,系统的线性部分受结构摄动以区间传递函数表示,而其非线性(不确定)反馈函数在一个扇区内。将鲁棒性分析的现代结果与经典的圆判据相结合,给出检验上述系统鲁棒绝对稳定性的方法。这个方法只用到16个特别选出的传递函数的奈氏曲线。这个数目不随系统的线性部分的阶次增高而加大,在某些特别情况下却可能更小。于是,将原问题的计算复杂性降到了一个非常低的水平。

Consider robust absolute stability for nonlinear closed-loop systems in which the linear parts are subjected to structured perturbations and described by interval transfer functions while the nonlinear (uncertain) feedback functions lie in a sector, Combining modern results on robustness analysis and the classical circle criterion, we present a criterion to examine the robust absolute stability of the systems mentioned above. Our criteria only use the frequency-domain properties of the 16 transfer functions specifically choose within the interval transfer functions. When the perturbations in the linear parts occur only on the numerators or denominators of the transfer function, it is enough to use 4 specific transfer functions. In this way, computational complexity in the original problem is reduced to an extremely low level.