频域结构不确定性模型有效性分析──正切结构Nevanlinna-Pick插值法

Frequency Domain Validation of Structured Uncertain Models－A Structured Tangential Nevanlinna-Pick Interpolation Approach

利用正切结构Nevanlinna-Pick插值理论，研究了扰动集有结构的具有线性分式传递函数的模型有效性分析问题．模型有效性与参数辨识相结合是本领域目前的研究热点问题，故这里讨论的模型集的不确定性不仅有扰动集的不确定，还有不易观测的部分名义模型的不确定．我们将这类模型集的有效性分析问题转化为双线性矩阵不等式（BMI）求解问题，构造了双迭代算法进行求解，并给出了算法的理论分析，得到了在有限步迭代后可判定模型集是否无效的结论．

The frequency domain model validation for structured uncertain is discussed with the structured tangentialNevanlinna-Pick interpolation theory.The Model uncertainty include both the part of normal model uneasy to measured uncertainty and the perturbations uncertainty,for the combination of identification and validation is a new point in this domain.We convertthis problem into finding a feasible solution of a biaffine matrix inequality (BMI),It can be solved by a biaffine iteration algo-rithm.The theoretical analysis show that we can drove the conclusion of whether the uncertain model set is invalidation in finitestep.