A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems
A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems
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DOI：
10.1109/acc.2003.1239126
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发表时间：
2003-06
期刊：
影响因子：
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通讯作者：
Y. Ebihara;T. Hagiwara
中科院分区：
文献类型：
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作者：
Y. Ebihara;T. Hagiwara
研究了基于LMI的参数不确定线性定常系统的鲁棒性能分析。在系统的系数矩阵是仿射的不确定参数的情况下，标准的线性矩阵不等式有助于处理这样的分析问题，只要我们接受二次稳定的概念。另一方面，在合理的参数依赖的情况下，标准的LMI进行一些不足，因此我们需要另一个努力，以获得数值上易于处理的条件。本文表明，最近开发的扩张的LMI是有效的攻击这种强大的性能分析问题。事实上，应用扩张的线性矩阵不等式直接导致数值上易于处理的条件，无论形式的依赖于不确定的参数。此外，扩张的线性矩阵不等式使我们能够采用参数相关的李雅普诺夫变量来测试鲁棒性能，这是已知的是相当有效的，以减轻保守性所造成的二次（参数无关）李雅普诺夫变量。
This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMIs are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMIs carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMIs are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMIs leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMIs enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.