Stability conditions for infinite networks of nonlinear systems and their application for stabilization
Stability conditions for infinite networks of nonlinear systems and their application for stabilization
复制标题
DOI：
10.1016/j.automatica.2019.108643
复制
发表时间：
2020-02-01
期刊：
影响因子：
6.4
通讯作者：
Pavlichkov, Svyatoslav
中科院分区：
文献类型：
--
作者：
Dashkovskiy, Sergey;Pavlichkov, Svyatoslav
我们为由一组可数互连的常微分方程非线性子系统组成的无限网络引入了 l(无穷大) 输入状态稳定性的新概念。我们假设整个状态向量是 l(无穷大) 的元素，并且每个子系统都是输入状态稳定的，而其整个扰动输入（包括与其他子系统可能的互连）的维数是有限的。我们的第一个主要结果为此类无限维网络的 l（无穷大）输入状态稳定性提供了条件。在我们的第二个主要结果中，我们解决了由具有不可控线性化的互连下三角形式子系统组成的此类网络的分散l（无穷大）-ISS稳定问题。为了应用我们的第一个主要结果并获得第二个主要结果，我们为每个单独的代理构建了一个反馈，这满足了我们新的稳定性条件。这产生了整个网络的稳定性。我们的设计对于有限网络来说也是新的，这可以被视为一个重要的特例。 (C) 2019 Elsevier Ltd. 保留所有权利。
We introduce a new concept of l(infinity)-input-to-state stability for infinite networks composed of a countable set of interconnected nonlinear subsystems of ordinary differential equations. We suppose that the entire state vector is an element of l(infinity) and each subsystem is input-to-state stable whereas the dimension of its entire disturbance input including possible interconnections with other subsystems is finite. Our first main result provides conditions for l(infinity)-input-to-state stability of such infinite-dimensional networks. In our second main result, we solve the problem of decentralized l(infinity)-ISS stabilization for such networks composed of interconnected lower-triangular form subsystems with uncontrollable linearization. To apply our first main result and obtain the second one, we construct a feedback for each individual agent, which satisfies our new stability conditions. This yields the stabilization of the entire network. Our design is also new for finite networks and this can be considered as an important special case. (C) 2019 Elsevier Ltd. All rights reserved.