论文标题
从LQR到静态输出反馈：一种新的LMI方法
From LQR to Static Output Feedback: a New LMI Approach
论文作者
论文摘要
本文提出了一种新的线性矩阵不等式（LMI），用于静态输出反馈控制，假设先前已经为系统设计了线性二次调节器（LQR）。主要思想是将二次候选lyapunov函数用于通过求解riccati方程的唯一正定矩阵参数化的闭环系统。还将证明相反的结果，可以保证存在矩阵是否存在静态输出反馈，以验证LMI。然后，提出的方法将扩展到H1控制问题的静态输出反馈的设计。除了证明相反结果的充分条件外，提出的方法论还有另外四个主要优点。首先，它在计算上是可处理的。其次，可以使用加权矩阵，并以与LQR设计类似的方式获得解决方案。第三，与文献中提出的其他LMI方法相比，该方法具有非常简单的LMI结构。最后，对于输出等于状态的情况，显示LQR解决方案验证了所提出的LMI。因此，静态输出反馈包括在可用状态时作为特殊情况（是所需属性）的特殊情况。几个例子表明，该方法始终取得成功，并且在实践中效果很好。
This paper proposes a new Linear Matrix Inequality (LMI) for static output feedback control assuming that a Linear Quadratic Regulator (LQR) has been previously designed for the system. The main idea is to use a quadratic candidate Lyapunov function for the closed-loop system parameterized by the unique positive definite matrix that solves the Riccati equation. A converse result will also be proved guaranteeing the existence of matrices verifying the LMI if the system is static output feedback stabilizable. The proposed method will then be extended to the design of static output feedback for the H1 control problem. Besides being a sufficient condition for which a converse result is proved, there are another four main advantages of the proposed methodology. First, it is computationally tractable. Second, one can use weighting matrices and obtain a solution in a similar way to LQR design. Third, the proposed method has an extremely simple LMI structure when compared with other LMI methods proposed in the literature. Finally, for the cases where the output is equal to the state it is shown that the LQR solution verifies the proposed LMI. Therefore, the static output feedback includes the LQR solution as a special case when the state is available, which is a desired property. Several examples show that the method is consistently successful and works well in practice.
