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首页> 外文期刊>The Journal of the Astronautical Sciences >Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay
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Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

机译：时变反馈时滞未知的非线性系统的稳定性

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This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.
机译：本文考虑稳定一类非线性系统的问题，该系统具有未知的有限时滞反馈，其中时变延迟为1）分段常数2）以有限制的速率连续。我们还考虑将这些结果应用于刚体姿态动力学的稳定化。在第一种情况下，反馈中的时间延迟被专门建模为在任意一组较大的未知常数值之间以已知的严格上限进行切换。反馈是延迟状态的线性函数。在具有切换延迟反馈的线性系统的情况下，使用完整的Lyapunov-Krasovskii（L-K）功能方法提出了平均停留时间结果的新充分条件。此外，已证明具有非线性摄动的相应切换系统在适当选择的平均停留时间内，在特征明确的吸引区域内是指数稳定的。在第二种情况下，完整类型L-K函数的概念被扩展到一类具有未知时变时延的非线性时滞系统。对于所有小于已知上限的时间延迟值，此扩展确保了控制设计中的时间延迟稳定性鲁棒性。使用模型转换是为了将非线性系统划分为名义线性部分，该名义线性部分具有有限摄动，呈指数稳定。我们获得了足够的条件，可以确保在吸引力估算区域内的指数稳定性。提出了一种评估充足条件的建设性方法，并与相应的常数和分段常数延迟进行了比较。数值模拟表明了本文的理论结果。

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