具有多线性相关系数扰动的有理函数的严格正实不变性判据及其应用

INVARIANCE OF STRICTLY POSITIVE REALNESS FOR RATIONAL FUNCTIONS WITH MULTILINEARLY DEPENDENT COEFFICIENT PERTURBATIONS AND ITS APPLICATIONS

传递函数的严格正实不变性分析，由于它在绝对稳定性分析中的重要作用，引起了人们的重视．该文考虑在多线性相关系数摄动下，有理函数族的严格正实不变性的判别问题．利用严格正实函数所具有的相位条件和映射定理．证明了在参数空间中判别该有理函数族保持严格正实不变性的顶点检验条件，并将这一结果应用于带参数不确定性的鲁里叶系统的绝对稳定性分析中．

The strictly positive realness (SPR) property of transfer functions is an important topic in control engineering and related fields, e. g., absolute stability and huperstability analysis of nonlinear systems. This paper discusses the problem of determining the invariance of SPR property for rational functions with multilinearly dependent coefficient perturbations. By using the Mapping Theorem and the phase conditions satisfied by SPR functions, it is proved that invariance of SPR property for a family of rational functions with multilinearly dependent coefficient perturbations is guaranteed if the functions with respect to the vertex values of perturbed parameters are SPR. The result is established in the parameter space,. and is applied to the analysis of absolute stability of a Lur'e system with parametric uncertainty.