Robust performance analysis of linear time-invariant parameter-dependent systems using higher-order Lyapunov functions
Robust performance analysis of linear time-invariant parameter-dependent systems using higher-order Lyapunov functions
复制标题
使用高阶 Lyapunov 函数对线性时不变参数相关系统进行鲁棒性能分析
DOI：
10.1109/acc.2005.1470025
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Masayuki Sato
中科院分区：
文献类型：
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作者：
Masayuki Sato
本文研究了状态空间表示中的系数矩阵在参数的负幂级数和正幂级数上都与参数相关，且参数位于给定凸域中的线性定常参数相关系统的鲁棒稳定性/性能分析。为了分析鲁棒稳定性/性能，我们使用了负幂级数和正幂级数中参数相关的参数相关Lyapunov函数，并通过参数仿射线性矩阵不等式推导了它们的充分条件。虽然我们的公式比以前的工作有更大的数值复杂性，但它们包含了基于双二次稳定性的公式，这是为了获得更少的保守条件而提出的，以及传统的二次稳定性。最后给出了数值算例，与现有方法进行了比较，证明了所提方法的有效性。
This paper studies the robust stability/performance analysis of linear time-invariant parameter-dependent systems for which the coefficient matrices in the state-space representations are parameter-dependent in negative as well as positive power series of parameters, and whose parameters are supposed to lie in a given convex region. To analyze the robust stability/performance, we use parameter-dependent Lyapunov functions that are parameter-dependent in negative as well as positive power series, and derive sufficient conditions for them via parametrically affine linear matrix inequalities. Although our formulae have greater numerical complexity than previous works, they encompass formulae based on biquadratic stability, which has been proposed to obtain less conservative conditions, and conventional quadratic stability. We present numerical examples that demonstrate the effectiveness of our proposed methods compared with existing methods.
DOI：
10.1109/acc.2003.1239126
发表时间：
2003-06
期刊：
Proceedings of the 2003 American Control Conference, 2003.
影响因子：
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作者：
Y. Ebihara;T. Hagiwara
通讯作者：
Y. Ebihara;T. Hagiwara