A linear matrix inequality approach to synthesizing low order l/sup 1/ controllers
A linear matrix inequality approach to synthesizing low order l/sup 1/ controllers
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合成低阶 l/sup 1/ 控制器的线性矩阵不等式方法
DOI：
10.1109/cdc.1996.572846
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
M. Holmes
中科院分区：
文献类型：
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作者：
J. Bu;M. Sznaier;M. Holmes
的l/sup 1/控制理论是有吸引力的，因为它允许直接将时域规格到控制器的合成过程和prograshes一个完整的解决方案的鲁棒性能问题。此外，在SISO的情况下，合成过程可以转换成一个有限维线性规划问题，并有效地解决。MIMO情况可以通过添加虚拟输入和输出来迭代地解决，以将问题重铸为一个块的形式。然而，众所周知，与H/sub 2/和H/sub /spl infin//情况相反，最优l/sup 1/控制器可以具有任意高阶，即使当对象的状态可用于反馈时。在本文中，我们解决的问题，设计低阶次优l/sup 1/控制器使用线性矩阵不等式（LMI）优化方法。主要结果表明，在状态反馈情况下，次优控制器是静态的，而在输出反馈情况下，它具有相同的阶数的对象。在这两种情况下，合成过程涉及解决LMI可行性问题和（0，1）上的标量最小化。
The l/sup 1/ control theory is appealing, since it allows for directly incorporating time-domain specifications into the controller synthesis procedure and furnishes a complete solution to the robust performance problem. Moreover, in the SISO case, the synthesis procedure can be recast into a finite-dimensional linear programming problem and solved efficiently. The MIMO case can be solved iteratively by adding fictitious inputs and outputs to recast the problem into an one-block form. However, it is well known that, in contrast to the H/sub 2/ and H/sub /spl infin// cases, optimal l/sup 1/ controllers can have arbitrarily high order, even when the states of the plant are available for feedback. In this paper, we address the problem of designing low order suboptimal l/sup 1/ controllers using a linear matrix inequality (LMI) optimization approach. The main results show that, in the state-feedback case, the suboptimal controller is static, while in the output-feedback case it has the same order as that of the plant. In both cases the synthesis process involves solving an LMI feasibility problem and a scalar minimization over (0,1).