A characterization of integral input-to-state stability
A characterization of integral input-to-state stability
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DOI：
10.1109/9.863594
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发表时间：
2000-06-01
影响因子：
6.8
通讯作者：
Wang, Y
中科院分区：
文献类型：
--
作者：
Angeli, D;Sontag, ED;Wang, Y
输入-状态稳定(ISS)的概念现在被认为是非线性系统分析的一个核心概念。它给出了有限增益关于上确界范数的非线性推广，也给出了有限L-2增益的非线性推广。它在递归设计、互质分解、非最小相位系统的控制器等许多领域发挥着核心作用。本文研究了一种较新的概念--积分输入-状态稳定性。当对输入使用积分范数但状态的至上范数时，IISS的概念推广了有限增益的概念，在这个意义上推广了线性“H-2”理论。它使人们即使在某些形式的非线性共振存在的情况下也能量化灵敏度。在这里，我们得到了IISS性质的几个充要刻划，用耗散不等式和其他可选的非平凡刻划表示。这些特征表明，整体投入对状态的稳定性是一个最自然的概念，最终可能发挥至少与国际空间站相媲美的作用，如果不是比国际空间站更重要的话。
The notion of input-to-state stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite L-2 gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that of integral input-to-state stability (iISS), is studied. The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear "H-2" theory. It allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance. We obtain here several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations. These characterizations serve to show that integral input-to-state stability is a most natural concept, one that might eventually play a role at least comparable to, if not even more important than, ISS.