控制理论中的频率定理:Kalman-Yakubovich引理

介绍了Kalman-Yakubovich引理，重点强调了引理中的频域条件与状态空间条件之间的等价关系，基于这种等价关系，可以直接求得当前控制理论中的几个重要定理，正实引理，有界实引理和Popov判据，还给出了代数Riccati方程有解的频率判据。由于当前LMI法的进展，所以这种等价关系已是频率定理的主要特色，对上述重要定理的推导可以作为频率定理推广应用于其他设计问题时的范例。

The Frequency Theorem in control theory: Kalman-Yakubovich lemma

This paper presents the Kalman-Yakubovich Lemma with emphasis on the equivalent relationship between frequency-domain conditions and those of state-space form. Based on these relationships, some important theorems in modern control theory such as Positive Real Lemma, Bounded Real Lemma, and Popov criterion can be derived directly, as illustrated in this paper. The frequency criterion for the solvability of an algebraic Riccati equation is also derived. Because of the recent development of the LMI method, the equivalent relationship between frequency-domain and state-space becomes the outstanding feature of the Frequency Theorem. The derivations presented in this paper can serve as examples for new applications.