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摘要: 研究了李雅普诺夫函数的选择对求解系统H∞范数的影响，提出了一种李雅普诺夫函数的直接优化方法，该方法通过优化黎卡提不等式中的李雅普诺夫函数，给出了H∞范数的通用解析表达式，实现了二阶系统H∞范数的精确求解.不同于需要繁琐优化过程的线性矩阵不等式（Linear matrix inequality，LMI）方法，本文提供了一种有效的途径以直接求解系统H∞范数.
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关键词:
- H∞范数 /
- Lyapunov函数 /
- 线性系统 /
- Riccati不等式 /
- 鲁棒稳定性
Abstract: The paper studies the effect of the Lyapunov function selection on solving the system H∞ norm. A Lyapunov function optimization method is presented. By optimizing the Lyapunov function in the Riccati inequality, the presented method gives the analytical expression for the H∞ norm, such that the H∞ norm of the second-order system can be accurately solved. Different from the linear matrix inequality approaches which need the complex optimization process, the paper provides an alternative way to directly get the H∞ norm.-
Key words:
- H∞ norm /
- Lyapunov function /
- linear system /
- Riccati inequality /
- robust stability
1) 本文责任编委 高会军 -
表 1 $H_{\infty}$范数分析($\alpha = 2$)
Table 1 $H_{\infty}$ norm analysis ($\alpha = 2$)
$\lambda$ $\nu$ MATLAB 定理4 稳态误差$\|A^{-1}\|$ 状态上界 2 6 0.626 0.626 0.307 0.626 2 4 0.626 0.626 0.419 0.626 2 2 0.626 0.626 0.588 0.626 2 1.2 0.626 0.626 0.626 0.626 2 1 0.622 0.622 0.622 0.622 2 0 0.501 0.501 0.501 0.501 
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