Characterizations of Input-to-State Stability for Infinite-Dimensional Systems
Characterizations of Input-to-State Stability for Infinite-Dimensional Systems
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DOI：
10.1109/tac.2017.2756341
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发表时间：
2017-01
影响因子：
6.8
通讯作者：
A. Mironchenko;Fabian R. Wirth
中科院分区：
文献类型：
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作者：
A. Mironchenko;Fabian R. Wirth
我们证明了一大类无限维控制系统的输入到状态稳定性（ISS）的特征，包括Banach空间上的发展方程，时滞系统，常微分方程（ODE）和切换系统的一些类别。这些刻画推广了Sontag和Wang对常微分系统证明的ISS准则。对于Banach空间中的微分方程的特殊情况下，我们证明了更广泛的标准ISS和应用这些结果表明，（在一些温和的限制）存在一个非强制性的ISS的李雅普诺夫函数意味着ISS。我们引入了新的概念，强ISS（sISS），这是相当于国际空间站在常微分方程的情况下，但严格弱于ISS在无限维的设置，并证明了几个标准的sISS属性。同时，我们通过反例证明了许多在常微分方程情形下有效的刻画对于一般的无穷维系统是不成立的。
We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay systems, ordinary differential equations (ODE), and switched systems. These characterizations generalize well-known criteria of ISS, proved by Sontag and Wang for ODE systems. For the special case of differential equations in Banach spaces, we prove even broader criteria for ISS and apply these results to show that (under some mild restrictions) the existence of a noncoercive ISS Lyapunov functions implies ISS. We introduce the new notion of strong ISS (sISS) that is equivalent to ISS in the ODE case, but is strictly weaker than ISS in the infinite-dimensional setting and prove several criteria for the sISS property. At the same time, we show by means of counterexamples that many characterizations, which are valid in the ODE case, are not true for general infinite-dimensional systems.