H_∞控制问题中RIC法和LMI法的一个比较

A comparison between RIC-based and LMI-based sysnthesis in H_∞ control problems

以弱阻尼系统为例，说明了Ｈ∞控制问题中ＲＩＣ法的零极点对消问题；然后通过分析ＬＭＩ法的特点，指出限制ＬＭＩ解的范数可以控制靠近虚轴的闭环极点，即可以通过函数ｈｉｎｆｌｍｉ（）本身的选项来控制极点位置，因此单用混合灵敏度同样可以解决弱阻尼系统的Ｈ∞控制问题，而不必如文［２］那样再增加极点配置的ＬＭＩ约束条件。

The problem of pole--zero cancellation in Riccati equation--based H_∞ synthesis is demonstrated with a lightly damped system. Then, the properties of LMI--based synthesis are discussed. It is pointed out that the system's closed--loop poles near the jw--axis can be controlled by the norms of the LMIs' solutions via the options of the function hinflmi() itself. Hence, the problem of H_∞ control of lightly damped system can be solved by mixed--sensitivity design alone, and needs no additional LMI constraints as used in [2].