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首页> 外文期刊>IEEE Transactions on Automatic Control >Stability of Systems With Uncertain Delays: A New 'Complete' Lyapunov-Krasovskii Functional
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Stability of Systems With Uncertain Delays: A New 'Complete' Lyapunov-Krasovskii Functional

机译：具有不确定延迟的系统的稳定性：新的“完全” Lyapunov-Krasovskii功能

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摘要

Stability of linear systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present note we combine a "complete" nominal LKF, the derivative of which along the trajectories depends on states and their derivatives, with the additional terms depending on the delay perturbation. The new method is applied to the case of multiple uncertain delays with one nonzero nominal value. Numerical examples illustrate the efficiency of the method.
机译：在时延的标称值恒定且非零的情况下，考虑具有不确定时变时滞的线性系统的稳定性。最近，引入了一种新的Lyapunov-Krasovskii泛函（LKF）构造：在适用于具有名义延迟的系统的标称LKF中，添加了与被摄动系统相对应的项，并且当延迟摄动接近于0时这些项消失了。在本说明中，我们结合了一个“完整的”名义LKF，其沿轨迹的导数取决于状态及其导数，而附加项则取决于延迟扰动。该新方法适用于具有一个非零标称值的多个不确定延迟的情况。数值算例说明了该方法的有效性。

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