Multi-Parameter Dependent Lyapunov Functions for the Stability Analysis of Parameter-Dependent LTI Systems

Multi-Parameter Dependent Lyapunov Functions for the Stability Analysis of Parameter-Dependent LTI Systems
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用于参数相关 LTI 系统稳定性分析的多参数相关 Lyapunov 函数

DOI：
10.1109/.2005.1467197
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发表时间：
2005
期刊：
Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005.
影响因子：
--
通讯作者：
P. Bliman
P. Bliman
中科院分区：
--
文献类型：
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作者：
X. Zhang;Panagiotis Tsiotras;P. Bliman

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本文证明了多参数仿射依赖LTI系统的鲁棒稳定性等价于多参数多项式依赖二次Lyapunov函数的存在性，该函数关于系统参数的已知有界次。在紧致连通集上测试多参数相关LTI系统的稳定性可以用两个有限维线性矩阵不等式(LMI)来表示
In this paper it is shown that robust stability of multiparameter affinely-dependent LTI systems is equivalent to the existence of a multi-parameter polynomially-dependent quadratic Lyapunov function of known, bounded degree in terms of the system parameters. Testing the stability of multi-parameter dependent LTI systems over a compact, connected set can be cast in terms of two finite-dimensional linear matrix inequalities (LMIs)