一类关联系统基于无源性的稳定性判据及其在生化反应网络中的应用
A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks
摘要：
研究了一类由生化反应网络驱动的关联非线性系统的稳定性问题。其中一个主要结果确定了网络的全局渐近稳定性的对角稳定性的“耗散矩阵”，其中包括信息的无源属性的子系统，网络的互连结构，和互联条款的迹象。这个稳定性测试包括我们以前的论文中提出的循环网络的“割线准则”，并将其扩展到由图表示的一般互连结构。第二个主要结果允许容纳状态产品。这种扩展使得新的稳定性准则适用于更广泛的一类模型，即使在循环系统的情况下。新的稳定性测试上的丝裂原活化蛋白激酶（MAPK）级联模型，并在一个分支的互连结构的动机代谢网络。最后，另一个结果解决了稳定性的鲁棒性的存在下，扩散项在一个房室系统的相同的系统。
英文摘要：
This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems.
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