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在实际控制系统中,常常需要关注局部频段下的性能指标,而现有的频率加权方法缺乏针对性。由于时滞现象的普遍性及时滞条件下频域分析的复杂性,需要进一步给出时滞系统在局部频段下的H_∞性能分析方法。为研究线性时滞系统在局部频段下的性能,基于广义Kalman-Yakubovich-Popov引理及窗口频域H_∞范数的概念,给出了线性时滞系统的广义界实定理。针对不同频率范围,给出适用于不同频率条件的频域分析线性矩阵不等式判据。最后通过仿真实例,表明窗口频域分析比传统的全频段H_∞分析具有针对性和有效性。
In the actual control system, often need to pay attention to the performance index under the local frequency band, and the existing frequency weighting method lacks pertinence. Due to the universality of the time lag phenomenon and the complexity of the frequency domain analysis under the condition of time lag, it is necessary to further give the H_∞ performance analysis method of the time-delay system in the local frequency band. In order to study the performance of linear time-delay systems in local frequency bands, a generalized bound theorem for linear time-delay systems is given based on the concepts of generalized Kalman-Yakubovich-Popov lemma and H_∞ norm in window frequency domain. For different frequency ranges, the criterion of linear matrix inequality for frequency domain analysis is given for different frequency conditions. Finally, a simulation example is given to show that the window frequency domain analysis is more specific and effective than the traditional full band H_∞ analysis.