控制理论中的频率定理(Kalman-Yakubovich引理)

Frequency Theorem (Kalman-Yakubovich Lemma)in Control Theory

频率定理（Kalman－Yakubovich引理）是控制理论中的重要结果之一．它给出了Lur’e方程和Riccati方程可解的一个充分必要条件．本文简要叙述了频率定理建立和发展的历史，描述了它在非线性系统绝对稳定性理论，线性二次型最优控制和自适应控制理论中的部分应用．

Frequency theorem (or Kalman-Yakubovich lemma) is one of the most important results in the control theory. It gives a sufficient and necessary condition for the solubility of Lur'e equation and Riccati equation. In this paper,we set forth the history of its establishment and development. We expound its application in the absolutely stability theory,the optimal control theory and the adaptive control theory.