This article proposes a hybrid search (involving the performance level and a positive scalar variable in sequence) based method for synthesis of linear time-invariant (LTI) static output feedback (SOF) controllers for a class of linear systems with norm-bounded time-varying parametric uncertainties. Using an available extended linear matrix inequality (LMI) formulation of bounded real lemma, a new sufficient condition in terms of LMIs is obtained for existence of SOF controllers, where a triangular structure in the variable part of the Lyapunov matrix is introduced, unlike the diagonal structure existing in direct synthesis methods in literature. To obtain as less as possible, the part of the Lyapunov matrix which is kept fixed while computing the variable part is first obtained using a -search based method. Then with this fixed part, the final variable triangular part of the Lyapunov matrix is obtained using a single positive scalar search based LMI method to further reduce . The efficacy of the proposed method is studied on a number of benchmark examples. The method is also extended for structured SOF design. Finally, the proposed method is applied to design two-degree-of-freedom (2-DOF) multivariable proportional-integral-derivative (PID) controllers for compensation of norm-bounded uncertain plants. A case study on designing roll–pitch–yaw integrated missile autopilots is also considered to show the efficacy of the proposed multivariable PID compensation.

中文翻译：

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基于混合搜索的不确定系统静态输出反馈控制器综合，并应用于多变量 PID 控制

本文提出了一种基于混合搜索（涉及性能水平和序列中的正标量变量）的方法，用于合成一类具有范数有界时间的线性系统的线性时不变 (LTI) 静态输出反馈 (SOF) 控制器。不同的参数不确定性。使用有界实引理的可用扩展线性矩阵不等式 (LMI) 公式，获得了存在 SOF 控制器的 LMI 方面的新充分条件，其中在 Lyapunov 矩阵的变量部分引入了三角形结构，与对角线不同文献中直接合成方法中存在的结构。获得尽可能少地，首先使用基于搜索的方法获得在计算可变部分时保持固定的李雅普诺夫矩阵部分。然后利用这个固定部分，使用基于单正标量搜索的 LMI 方法获得 Lyapunov 矩阵的最终可变三角形部分，以进一步减少。在许多基准示例上研究了所提出方法的有效性。该方法还扩展到结构化 SOF 设计。最后，将所提出的方法应用于设计二自由度 (2-DOF) 多变量比例积分微分 (PID) 控制器范数有界不确定植物的补偿。一个设计横滚-俯仰-偏航集成导弹自动驾驶仪的案例研究也被认为显示了所提出的多变量 PID 补偿的有效性。