L1 synthesis of a static output controller for positive systems by LMI iteration
L1 synthesis of a static output controller for positive systems by LMI iteration
复制标题
DOI：
10.1002/rnc.3956
复制
发表时间：
2018-03
影响因子：
3.9
通讯作者：
M. Saeki
中科院分区：
文献类型：
--
作者：
M. Saeki
提出了一种寻找静态输出反馈增益的方法，该方法使反馈系统为正，并使L1增益最小。寻找静态输出反馈增益的问题有三个方面：稳定系统，使系统为正，然后最小化L1增益。每个子问题由关于反馈增益和李雅普诺夫矩阵或向量的双线性矩阵不等式描述。利用凸-凹分解方法推导出了满足双线性矩阵不等式的线性矩阵不等式（LMI），并通过迭代求解LMI得到反馈增益序列.保证每个算法的设计参数上界序列是单调非增的。类似地，使用另一个凸-凹分解和PK迭代为每个子问题导出另外2个LMI。通过几个数值例子说明了这些算法的有效性。
An approach to find a static output feedback gain that makes the feedback system positive and minimizes the L1 gain is proposed. The problem of finding a static output feedback gain has 3 aspects: stabilizing the system, making the system positive, and then minimizing the L1 gain. Each subproblem is described by bilinear matrix inequality with respect to the feedback gain and the Lyapunov matrix or vector. Linear matrix inequality (LMI) that is sufficient to satisfy bilinear matrix inequality is derived using a convex‐concave decomposition, and the feedback gain sequence is calculated by an iterative solution of LMI. The sequence of the upper bounds on the design parameter is guaranteed to be monotonically nonincreasing for each algorithm. Similarly, 2 other LMIs are derived for each subproblem using another convex‐concave decomposition and PK iteration. The effectiveness of these algorithms is illustrated via several numerical examples.