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D-K算法是结构奇异值(μ)方法的主要实现方式,存在着求解条件较苛刻、系统适用性差的问题,针对D-K算法应用的局限性,提出将线性矩阵不等式(LMI)用于D-K算法的改进,即通过Schur引理与有界实引理得到了结构奇异值上界的LMI判据,利用消元法得到了输出反馈的H∞控制器,在此基础上通过D-K迭代解出输出反馈μ控制器,避免了因求解Riccati方程受到求解条件的限制以及待定参数选择好坏的影响,增强了D-K算法对一般系统的适用性并提高了求解效率。数值结果表明,该方法得到的输出反馈系统的鲁棒稳定性及鲁棒性能均优于传统D-K算法。
The DK algorithm is the main way to realize the structure singular value (μ) method. It has some problems such as harsh solution conditions and poor system applicability. In view of the limitations of the DK algorithm, this paper proposes an improved linear matrix inequality (LMI) algorithm for the DK algorithm The LMI criterion of the upper bound of the singular value of the structure is obtained by Schur’s lemma and bounded real lemmas. The H∞ controller of the output feedback is obtained by the elimination method, and on the basis of this, the output feedback μ The controller avoids the limitation of solving the Riccati equation and the choice of the parameters to be determined, and enhances the applicability of the DK algorithm to the general system and improves the efficiency of the solution. The numerical results show that the proposed robust robustness and robustness of the output feedback system are superior to the traditional D-K algorithm.