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首页> 外文期刊>IEEE Transactions on Automatic Control >Relaxed Conditions for the Input-to-State Stability of Switched Nonlinear Time-Varying Systems
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Relaxed Conditions for the Input-to-State Stability of Switched Nonlinear Time-Varying Systems

机译：切换非线性时变系统的输入至状态稳定性的松弛条件

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摘要

This technical note considers the problem of input-to-state stability (ISS) for switched nonlinear time-varying systems. First, a sufficient condition is proposed to verify the ISS of nonlinear time-varying systems by using an improved Lyapunov function. Then, the results obtained are extended to study the ISS of switched nonlinear time-varying systems. Three relaxed conditions are given by using the methods of multiple Lyapunov functions, minimum dwell time, and infinite switchings, respectively. Comparing with the existing results, the conditions obtained have two relaxations, i.e., the derivative of Lyapunov functions of subsystems are allowed to be indefinite, and all subsystems are allowed to be unstable in the case of infinite switchings. All results obtained also be used to study the uniformly asymptotic stability (UAS) of systems. Finally, a numerical example is given to illustrate the theoretical results.
机译：本技术说明考虑了切换非线性时变系统的输入状态稳定性（ISS）问题。首先，提出了利用改进的Lyapunov函数验证非线性时变系统的ISS的充分条件。然后，将获得的结果扩展到研究切换非线性时变系统的ISS。通过使用多个Lyapunov函数，最小停留时间和无限切换的方法分别给出了三个松弛条件。与现有结果相比，获得的条件有两个松弛，即，允许子系统的Lyapunov函数的导数是不确定的，并且在无限切换的情况下，所有子系统都可以是不稳定的。获得的所有结果也可用于研究系统的均匀渐近稳定性（UAS）。最后，通过数值例子说明了理论结果。

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