Invariance of Strictly Positive Realness for Rational Functions with Multilinearly Dependent Coefficient Perturbations and its Applications
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

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.