Absolute stability with a generalized sector condition.

被引：70

作者：

Hu, TS ^{[1
]}

Huang, B ^{[1
]}

Lin, ZL ^{[1
]}

机构：

[1] Univ Virginia, Dept Elect & Comp Engn, Charlottesville, VA 22904 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2004年 / 49卷 / 04期

基金：

美国国家科学基金会;

关键词：

absolute contractive invariance (ACI); absolute stability; concave function; convex function; generalized sector;

D O I：

10.1109/TAC.2004.825657

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper generalizes the linear sector in the classical absolute stability theory to a sector bounded by concave/convex functions. This generalization allows more flexible or more specific description of the nonlinearity and will thus reduce the conservatism in the estimation of the domain of attraction. We introduce the notions of generalized sector and absolute contractive invariance for estimating the domain of attraction of the origin. Necessary and sufficient conditions are identified under which an ellipsoid is absolutely contractively invariant. In the case that the sector is bounded by piecewise linear concave/convex functions, these conditions can be exactly stated as linear matrix inequalities. Moreover, if we have a set of absolutely contractively invariant (ACI) ellipsoids, then their convex hull is also ACI and inside the domain of attraction. We also present optimization technique to maximize the absolutely contractively invariant ellipsoids for the purpose of estimating the domain of attraction. The effectiveness of the proposed method is illustrated with examples.

引用

页码：535 / 548

页数：14

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