Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations
Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations
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DOI：
10.1109/9.975496
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发表时间：
2001-12
期刊：
影响因子：
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通讯作者：
P. Apkarian;H. Tuan;J. Bernussou
中科院分区：
文献类型：
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作者：
P. Apkarian;H. Tuan;J. Bernussou
本说明描述了一个新的框架，分析和综合控制系统，这构成了一个真正的连续时间扩展的结果，只有在离散时间。与以前的结果相比，所提出的方法涉及一个特定的变换的李雅普诺夫变量和倒数的投影引理的变体，除了经典的线性化变换的控制器数据。对于鲁棒分析与综合、多通道H/sub 2/ stateand输出反馈综合等问题，该方法可得到保守性较低的线性矩阵不等式（LMI）特征。这是因为在这种新方法中，在某种程度上排除了使用单个李雅普诺夫函数的技术限制。此外，该方法为使用早期技术无法处理的问题提供了新的潜力。一个重要的例子是混合Lyapunov型约束的特征结构配置问题，给出了一个简单易行的公式。
This note describes a new framework for the analysis and synthesis of control systems, which constitutes a genuine continuous-time extension of results that are only available in discrete time. In contrast to earlier results the proposed methods involve a specific transformation on the Lyapunov variables and a reciprocal variant of the projection lemma, in addition to the classical linearizing transformations on the controller data. For a wide range of problems including robust analysis and synthesis, multichannel H/sub 2/ stateand output-feedback syntheses, the approach leads to potentially less conservative linear matrix inequality (LMI) characterizations. This comes from the fact that the technical restriction of using a single Lyapunov function is to some extent ruled out in this new approach. Moreover, the approach offers new potentials for problems that cannot be handled using earlier techniques. An important instance is the eigenstructure assignment problem blended with Lyapunov-type constraints which is given a simple and tractable formulation.