Computer generated Lyapunov functions for a class of nonlinear systems

Computer generated Lyapunov functions for a class of nonlinear systems
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计算机生成一类非线性系统的李亚普诺夫函数

DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
H. Haneda
H. Haneda
中科院分区：
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文献类型：
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作者：
Y. Ohta;H. Imanishi;L. Gong;H. Haneda

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研究一类非线性动力系统的李雅普诺夫函数的构造问题。这个问题被简化为构造一个满足某些条件的多面体。对扇区条件的概念进行了推广，使用一组分段线性函数对给定的非线性函数求值成为可能。这种改进大大降低了非线性系统稳定性分析中的保守性。提出了构造这种多面体的两种算法，并给出了两个例子来证明结果的有效性。>
The problem of constructing Lyapunov functions for a class of nonlinear dynamical systems is considered. The problem is reduced to the construction of a polytope satisfying some conditions. A generalization of the concept of sector condition that it makes possible to evaluate a given nonlinear function by using a set of piecewise-linear functions is proposed. This improvement greatly reduces the conservatism in the stability analysis of nonlinear systems. Two algorithms for constructing such polytopes are proposed, and two examples are shown to demonstrate the usefulness of the results. >