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Robust Stability/Performance Analysis for Linear Time-Invariant Polynomially Parameter-Dependent Systems using Polynomially Parameter-Dependent Lyapunov Functions

机译：基于多项式参数相关的Lyapunov函数的线性时不变多项式参数相关系统的鲁棒稳定性/性能分析

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This paper addresses robust stability, H2 performance, and Hinfin performance analysis for linear time-invariant parameter-dependent (LTIPD) systems using parameter-dependent Lyapunov functions (PDLFs). The state-space matrices of the LTIPD systems are set to be parameter-dependent in negative as well as positive power series with respect to parameters, and PDLFs are also set to be parameter-dependent in negative as well as positive power series with respect to parameters. Our results are derived using "slack variables" and restricting them to be parameter-independent, therefore, they are only sufficient conditions for the original analysis problems. However, we demonstrate the effectiveness of our results with randomly generated numerical examples and several numerical examples which are borrowed from existing papers
机译：本文介绍了使用参数依赖的Lyapunov函数（PDLF）对线性时不变参数依赖（LTIPD）系统的鲁棒稳定性，H 2 性能和H infin 性能分析。 LTIPD系统的状态空间矩阵被设置为与参数有关的参数为负数和正幂序列，而PDLF也被设置为与参数有关的参数的负数和正幂序列。参数。我们的结果是使用“松弛变量”导出的，并将它们限制为与参数无关，因此，它们仅是原始分析问题的充分条件。但是，我们通过随机生成的数值示例以及从现有论文中借用的几个数值示例来证明我们的结果的有效性。

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