Diagonal stability of a class of cyclic systems and its connection with the secant criterion
Diagonal stability of a class of cyclic systems and its connection with the secant criterion
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DOI：
10.1016/j.automatica.2006.04.009
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发表时间：
2006-09-01
期刊：
影响因子：
6.4
通讯作者：
Sontag, Eduardo D.
中科院分区：
文献类型：
--
作者：
Arcak, Murat;Sontag, Eduardo D.
我们考虑一类具有循环互连结构的系统，该结构在某些生化反应的动态模型中出现。我们首先表明，一个“割线”的局部稳定性的标准，在文献中较早推出，实际上是对角稳定的相应类别的矩阵的一个必要和充分条件。然后，我们重新审视最近的推广这一标准输出严格无源系统，并恢复相同的稳定性条件，使用我们的对角稳定性结果作为一种工具，用于构建一个李雅普诺夫函数。使用这个程序的李雅普诺夫建设，我们展示了行业的非线性循环系统类，并刻画其全局稳定性。(C)2006爱思唯尔有限公司保留所有权利。
We consider a class of systems with a cyclic interconnection structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a "secant" criterion for local stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent generalization of this criterion to output strictly passive systems, and recover the same stability condition using our diagonal stability result as a tool for constructing a Lyapunov function. Using this procedure for Lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties. (C) 2006 Elsevier Ltd. All rights reserved.