Local stability of composite systems--Frequency-domain condition and estimate of the domain of attraction
Local stability of composite systems--Frequency-domain condition and estimate of the domain of attraction
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DOI：
10.1109/tac.1980.1102464
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发表时间：
1980-10
影响因子：
6.8
通讯作者：
M. Saeki;M. Araki;B. Kondo
中科院分区：
文献类型：
--
作者：
M. Saeki;M. Araki;B. Kondo
本文研究的是这样的组合系统，其子系统包含一个非线性，每个子系统的连接是标量输出的函数。在每个非线性项满足扇形条件、关联项线性有界以及子系统的线性部分可能具有不稳定极点的假设下，给出了保证局部渐近稳定的频域条件.在推导上述结果时，构造子系统的这种李雅普诺夫函数，使得它们的加权和是整个系统的李雅普诺夫函数。研究了基于上述李雅普诺夫函数的吸引域估计方法。当非线性项的界在整个空间都成立，且线性项没有不稳定极点时，本文的条件与Araki以前得到的L2稳定性条件是一致的.
This paper is concerned with such composite systems whose subsystems contain one nonlinearity each and whose interconnections are functions of the scalar outputs of subsystems. A frequency-domain condition which assures local asymptotic stability is given under the assumptions that each nonlinearity satisfies a sector condition, that interconnections are linearly bounded, and that linear parts of subsystems may have unstable poles. In deriving the above result, such Lyapunov functions of subsystems are constructed so that their weighted sum is a Lyapunov function of the overall system. A method to estimate the domain Of attraction based on the above Lyapunov functions is also studied. When the bounds on nonlinearities hold true in the entire space and when the linear parts do not have unstable poles, the present condition turns out to be the same with the L 2 -stability condition which was obtained before by Araki.