Input-to-state stability of impulsive and switching hybrid systems with time-delay
Input-to-state stability of impulsive and switching hybrid systems with time-delay
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DOI：
10.1016/j.automatica.2011.01.061
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发表时间：
2011-05
期刊：
影响因子：
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通讯作者：
Jun Liu;Xinzhi Liu;W. Xie
中科院分区：
文献类型：
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作者：
Jun Liu;Xinzhi Liu;W. Xie
本文利用多重Lyapunov-Krasovskii泛函方法研究了时滞脉冲开关混合系统的输入-状态稳定性和积分输入-状态稳定性。结果表明，即使控制连续动力学的所有子系统在没有脉冲的情况下都不是ISS/iISS，只要脉冲之间没有过长的间隔，即脉冲和开关信号满足驻留时间上界条件，脉冲也能在ISS/iISS意义下成功地稳定系统。此外，这些脉冲ISS/iISS镇定结果可以应用于任意大时滞系统。相反，在没有脉冲的情况下，当控制连续动力学的所有子系统都是ISS/iISS时，如果脉冲和开关不太频繁地发生，即脉冲和开关信号满足驻留时间下界条件，则可以保留ISS/iISS性质。给出了几个说明性的例子，并进行了数值模拟，以证明主要结果。
This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov–Krasovskii functionals. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense, provided that there are no overly long intervals between impulses, i.e., the impulsive and switching signal satisfies a dwell-time upper bound condition. Moreover, these impulsive ISS/iISS stabilization results can be applied to systems with arbitrarily large time-delays. Conversely, in the case when all the subsystems governing the continuous dynamics are ISS/iISS in the absence of impulses, the ISS/iISS properties can be retained if the impulses and switching do not occur too frequently, i.e., the impulsive and switching signal satisfies a dwell-time lower bound condition. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.