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Input-to-State Stability, Integral Input-to-State Stability, and Unbounded Level Sets

机译:输入到状态稳定性,积分输入到状态稳定性和无限级别集

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We provide partial Lyapunov characterizations for a recently proposed generalization of input-to-state and integral input-to-state stability (ISS and iISS, respectively). This generalization relies on the notion of stability with respect to two measures originally introduced by Movchan [1960]. We show that the two classical Lyapunov characterizations of ISS-type properties, i.e., decrease conditions in an implication or dissipative form, correspond to ISS and iISS, respectively. We also demonstrate via an example that, for the generalization considered here, ISS does not necessarily imply iISS.
机译:我们提供部分Lyapunov特性,以便最近提出的输入到状态和积分输入到状态稳定性(ISS和IISS)。该概率依赖于Movchan最初引入的两种措施的稳定性概念[1960]。我们表明,ISS型属性的两个经典Lyapunov特征,即含义或耗散形式的条件,分别对应于ISS和IISS。我们还通过一个例子来证明,对于在此考虑的泛化,ISS并不一定意味着IISS。

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