Some new subclasses of systems having a common quadratic Lyapunov function and comparison of known subclasses

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) Pub Date : 2001-12-04 DOI:10.1109/CDC.2001.980578

Y. Mori, T. Mori, Y. Kuroe

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引用次数: 9

Abstract

A common quadratic Lyapunov function (CQLF) guarantees the asymptotic stability of a set of systems. A complete characterization of the set of systems with such a property have been unsuccessful (except for second-order systems). Thus, for both the continuous-time and discrete-time cases, several subsets of linear systems which have a CQLF are known. Some results indicate that there is a parallelism between the continuous-time case and the discrete-time case. In this paper, we show a new subclass for continuous-time systems which have a CQLF by using a property of M-matrices. We also show the discrete-time counterpart of the above new subclass. Next, it is shown that the whole class of continuous-time linear systems having a CQLF is connected directly with its discrete-time counterpart by using a bilinear transformation. For some known subclasses of systems having a CQLF, the transformation gives a one-to-one correspondence between the continuous-time and discrete-time cases. We further show relationships among the obtained results and other, known results.

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具有公共二次李雅普诺夫函数的系统的一些新子类及已知子类的比较

一个普通的二次Lyapunov函数(CQLF)保证了一组系统的渐近稳定性。具有这种性质的系统集的完整表征尚未成功(二阶系统除外)。因此，对于连续时间和离散时间两种情况，具有CQLF的线性系统的几个子集是已知的。一些结果表明，在连续时间情况下和离散时间情况下存在平行性。本文利用m矩阵的一个性质，给出了具有CQLF的连续时间系统的一个新的子类。我们还展示了上述新子类的离散时间对应物。其次，利用双线性变换证明了一类具有CQLF的连续时间线性系统与其离散时间系统直接相连。对于具有CQLF的系统的某些已知子类，该变换给出了连续时间和离散时间情况之间的一一对应关系。我们进一步展示了所得结果与其他已知结果之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

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