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以 S/KS问题为例分析了奇异问题的几种处理方法。指出权函数中有虚轴极点时可采用摄动的方法来处理,若对象中有虚轴极点则不能用这种摄动法。采用 LMI法虽然可直接处理奇异问题,但需另外设法控制靠近虚轴的极点。处理奇异问题的有效办法是扩展H∞控制,但是增加了求解问题的复杂度。
Taking the S / KS problem as an example, several processing methods of singularity problems are analyzed. It is pointed out that the method of perturbation can be used when there is a virtual axis in the weight function. If there is a virtual axis pole in the object, this perturbation method can not be used. Using the LMI method can deal directly with singular problems, but requires additional control of the pole near the imaginary axis. An effective way to deal with singular problems is to extend H∞ control, but it increases the complexity of solving the problem.