This paper is concerned with the $H_{\infty }$ control problem for Lipschitz nonlinear systems in the finite-frequency domain. Both parameter uncertainties and external disturbances are considered. In contrast to existing full-frequency methods, the proposed approach takes into account of the frequency information of disturbances during the design proceeding. Sufficient analysis conditions for the closed-loop system are firstly derived. Then, synthesis conditions are formulated in terms of linear matrix inequalities (LMIs). In fact, the control gain is designed to attenuate the influence of disturbances in different frequency ranges (low, middle and high). Finally, the model of the Chua circuit is used to validate the effectiveness of the proposed finite-frequency approach and to prove its superiority compared to the full-frequency counterpart.

本文与 $H_{\infty }$Lipschitz非线性系统的有限频域控制问题。同时考虑参数不确定性和外部干扰。与现有的全频方法相比，所提出的方法在设计过程中考虑了干扰的频率信息。首先推导了闭环系统的充分分析条件。然后，根据线性矩阵不等式（LMI）制定合成条件。实际上，控制增益旨在衰减不同频率范围（低，中和高）中的干扰影响。最后，使用Chua电路模型验证了所提出的有限频率方法的有效性，并证明了其与全频率方法相比的优越性。