A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions
A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions
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具有抽象初始条件的系统非线性小增益定理的推广
DOI：
10.23919/ecc.2013.6669591
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. French
中科院分区：
文献类型：
--
作者：
Jing Liu;M. French
我们考虑为具有抽象初始条件的系统开发一般非线性小增益定理。系统是根据双无限时间轴上的输入-输出对以集合理论方式定义的，并且初始条件（即时间零时的状态）的一般构造是根据负时间轴上的轨迹的等价类给出的。利用该公式，建立了稳定性性质与存在唯一性完全脱节的ISS型非线性小增益定理。我们提供一个说明性示例。
We consider the development of a general nonlinear small-gain theorem for systems with abstract initial conditions. Systems are defined in a set theoretic manner from input-output pairs on a doubly infinite time axis, and a general construction of the initial conditions (i.e. a state at time zero) is given in terms of an equivalence class of trajectories on the negative time axis. By using this formulation, an ISS-type nonlinear small-gain theorem is established with complete disconnection between the stability property and the existence, uniqueness properties. We provide an illustrative example.