带有不稳定子系统的切换非线性系统的积分输入状态稳定
Integral input-to-state stability of switched nonlinear systems with unstable subsystems

本文针对带有不稳定子系统的切换非线性系统研究了系统的积分输入状态稳定性问题. 应用导数不定的 类Lyapunov函数得出切换非线性系统的积分输入状态稳定. 导数不定的类Lyapunov函数方法比传统的导数正定 的Lyapunov函数的方法更具有一般性. 文中包含两种情况: 当所有子系统为积分输入状态稳定时, 切换非线性系统 是积分输入状态稳定的; 当部分子系统为非积分输入状态稳定时, 本文证明了切换非线性系统的积分输入状态稳 定. 最后应用一个仿真例子描述了所提结果的有效性.
This paper deals with the problem of integral input-to-state stability (iISS) for switched nonlinear systems with unstable subsystems. A Lyapunov-like function with indefinite derivative is introduced to derive the iISS of switched nonlinear systems, which generalizes the classic Lyapunov function with positive definite derivative. Two cases are considered. A switched nonlinear system is iISS if all subsystems are iISS. Moreover, if some of subsystems are not iISS, the iISS property is shown for the switched nonlinear systems. An illustrative example is presented to demonstrate the effectiveness of the main results.