用lmi估计多项式系统的吸引域

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) Pub Date : 2000-12-12 DOI:10.1109/CDC.2000.912314

B. Tibken

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引用次数: 105

摘要

研究非线性系统平稳点的稳定性是现代控制工程的核心问题。在这篇贡献中，我们展示了如何使用纯数学的一个分支——实代数几何的现代结果来计算多项式系统渐近稳定平稳点的吸引区域的子集。通过将该问题重新表述为线性矩阵不等式(LMI)，以数值稳定和有效的方式完成了该计算。为此，采用了实代数几何的结果。所提出的结果非常清楚地表明，非线性控制系统的多学科方法导致新的见解和新的强大的条件。最后，对全文进行了总结和展望。

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Estimation of the domain of attraction for polynomial systems via LMIs

Investigation of the stability properties of stationary points of nonlinear systems lies at the heart of modern control engineering. In this contribution we show how modern results of real algebraic geometry, a branch of pure mathematics, is used to compute subsets of the region of attraction of asymptotically stable stationary points of polynomial systems. This computation is done in a numerically stable and efficient way by reformulating the problem as a linear matrix inequality (LMI). For this reformulation results from real algebraic geometry are used. The results presented show very clearly that a multidisciplinary approach to nonlinear control systems leads to new insight and new powerful conditions. Some conclusions and an outlook finish the contribution.

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Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)

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