论文标题
非线性小增生定理，用于无限互连的输入稳定性
Nonlinear small-gain theorems for input-to-state stability of infinite interconnections
论文作者
论文摘要
我们考虑无限的异质网络，由可能无限维度的输入到州稳定子系统组成。我们表明，只要增益操作员满足某些小增益条件，网络是输入到州的稳定。我们表明，对于非线性系统的有限网络，该条件等效于所谓的增益操作员的强大小增益条件（因此，我们的结果扩展了有限网络的可用结果），对于具有线性增益运算符的无限网络，它们对应于增益运算符的频谱半径不到一个。我们提供有效的标准，该标准分别由线性和同质增益运算符支配，以线性增益的无限网络的投入到状态稳定性。
We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain condition. We show that for finite networks of nonlinear systems this condition is equivalent to the so-called strong small-gain condition of the gain operator (and thus our results extend available results for finite networks), and for infinite networks with a linear gain operator they correspond to the condition that the spectral radius of the gain operator is less than one. We provide efficient criteria for input-to-state stability of infinite networks with linear gains, governed by linear and homogeneous gain operators, respectively.
