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首页> 外文期刊>Automatic Control, IEEE Transactions on >Integral ISS for Switched Nonlinear Time-Varying Systems Using Indefinite Multiple Lyapunov Functions
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Integral ISS for Switched Nonlinear Time-Varying Systems Using Indefinite Multiple Lyapunov Functions

机译：使用不确定多重Lyapunov函数的切换非线性时变系统的积分ISS

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摘要

This paper is concerned with studying Lyapunov characterization of integral input-to-state stability (iISS) for switched nonlinear time-varying systems. Sufficient conditions are given to verify iISS for switched nonlinear time-varying systems under a time-varying state-dependent switching law designed, which allow all subsystems to be not integral input-to-state stable (iISS) and the time derivative of Lyapunov functions of individual subsystems to be indefinite. An indefinite multiple Lyapunov functions (iMLFs) method for analyzing the dynamic behavior of switched nonlinear time-varying systems is provided. Also, an iMLFs-based small-gain theorem for switched interconnected nonlinear time-varying systems is presented, where each lower dimensional subsystem is allowed to be not iISS, which extends the small-gain technique from its original nonswitched nonlinear time-invariant version to a switched nonlinear time-varying version. Finally, an illustrative example is used to demonstrate the feasibility of the theoretical results.
机译：本文涉及研究切换非线性时变系统的积分输入状态稳定性（iISS）的Lyapunov表征。在设计的随时间变化的状态相关切换定律下，给出了充分的条件来验证用于切换非线性时变系统的iISS，该条件允许所有子系统都不是积分的输入到状态稳定（iISS）和Lyapunov函数的时间导数各个子系统的数量不确定。提供了一种不确定的多重Lyapunov函数（iMLFs）方法，用于分析切换非线性时变系统的动态行为。此外，提出了基于iMLFs的开关互连非线性时变系统的小增益定理，其中每个低维子系统都不是iISS，这将小增益技术从其原始的非开关非线性时不变版本扩展到了开关非线性时变版本。最后，通过一个例子说明了理论结果的可行性。

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