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讨论了状态反馈H∞ 控制问题。给出了状态反馈H∞ 控制问题可解的必要条件 :判定一个由广义对象参数构成的矩阵的负定性。若该必要条件成立 ,则可构造出一个有限维参数化的矩阵对集合。当这个集合中包含有正定矩阵时 ,上述必要条件也是充分的。而且 ,当H∞ 控制问题可解时 ,所有可允的H∞ 控制器可由广义对象参数直接构造出来 ,改进了基于线性矩阵不等式 (LMI)的方法通过LMI的可行解来构造H∞ 控制器的结果。最后 ,给出了两个简单的例子 ,说明该方法的正确性
The state feedback H∞ control problem is discussed. The necessary conditions for solving the H∞ control problem with state feedback are given: Determine the negative definiteness of a matrix composed of generalized object parameters. If this necessary condition is satisfied, then a finite-dimensional parameterized matrix pair set can be constructed. The above necessary condition is also sufficient when this set contains positive definite matrices. Moreover, when the H∞ control problem is solvable, all permissible H∞ controllers can be constructed directly from generalized object parameters. The improved LMI-based method is used to construct the H∞ controller result. Finally, two simple examples are given to illustrate the correctness of the method