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首页> 外文期刊>Automatic Control, IEEE Transactions on >A Lyapunov Approach to Cascade Interconnection of Integral Input-to-State Stable Systems
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A Lyapunov Approach to Cascade Interconnection of Integral Input-to-State Stable Systems

机译：积分输入至状态稳定系统级联互连的Lyapunov方法

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This technical note deals with the stability of cascade interconnection of integral input-to-state (iISS) time-varying systems. A new technique to construct smooth Lyapunov functions of cascaded systems is proposed. From the construction, sufficient conditions for internal stability and stability with respect to external signals are derived. One of the derived conditions is a trade-off between slower convergence of the driving system and steeper input growth of the driven system. The trade-off is no more necessary if the speed of convergence of the driven system is not radially vanishing. The results are related to trajectory-based approaches and small-gain techniques for feedback interconnection. The difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts.
机译：本技术说明涉及整体输入状态（iISS）时变系统的级联互连的稳定性。提出了一种构造级联系统光滑Lyapunov函数的新技术。从该构造中，得出内部稳定性和相对于外部信号的稳定性的充分条件。导出的条件之一是在驱动系统的较慢收敛与驱动系统的较陡峭的输入增长之间进行权衡。如果从动系统的收敛速度没有在径向上消失，那么就不需要进行权衡。结果与基于轨迹的方法和反馈互连的小增益技术有关。从对自主零件收敛速度的要求来看，反馈情况和级联情况之间的差异。

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