基于结构Lyapunov矩阵的静态输出反馈镇定

线性时不变系统的静态输出反馈控制可行性等价于两个耦合的线性矩阵不等式解的存在性问题，这导致了一个非线性最优化问题，是无法直接求解的．针对线性时不变系统(LTI)，深入研究这两个矩阵不等式的关系，通过构造一个结构Lyapunov矩阵，给出了一个问题有解的充分条件，并在此基础上提出一个静态输出反馈镇定算法．利用线性矩阵不等式(LMI)方法，可直接求解出相应的输出反馈增益．数值实例证明了该方法的有效性．

Static output feedback stabilization based on structured Lyapunov matrix

The existence of a static output feedback for linear time-invariant systems is equivalent to the solvability of two coupled linear matrix inequalities (LMI), which is a non-linear optimization problem and can not be solved directly. For linear time-invariant (LTI) systems, the relation of the two inequalities is studied in detail and a structured Lyapunov matrix is proposed to derive a sufficient condition of the solvability for the stabilization problem. The corresponding algorithm is addressed, which is simple and solvable by LMI method. The simplicity and effectiveness of the proposed approach are demonstrated by some numerical examples.