关键词: H_∞范数, H_∞性能, H_∞控制, 干扰, 阻尼比, 时频交互综合分析

Abstract: Robust H_∞ performance is studied for a class of second-order linear systems with complex eigenvalues， especially the impact of imaginary part of complex eigenvalues on the H_∞ performance is studied. It is found that when the real part of the complex eigenvalues is fixed， the impact of the imaginary part of the complex eigenvalues on the H_∞ performance becomes little when the value of the imaginary part exceeds a threshold. Based on this observation， a fixed proportional relation between the imaginary part and the real part of the complex eigenvalues is found for a given system matrix under the framework of H_∞ performance. Referring to the classical control theory of second-order systems in frequency domain， the relationship between the selection ranges of damping ratio and the complex eigenvalue is further discussed in the framework of H_∞ performance， in which a reasonable explanation on the selection ranges of damping ratio is presented. This analysis procedure forms the time-frequency domain interaction synthesis method， which provides a theoretical guidance for the selection and determination of the desired closed-loop poles in the control theory based on the pole placement method.

Key words: H_∞ norm, H_∞ performance, H_∞ control, disturbance, damping ratio, time-frequency domain interaction synthesis method