This article addresses the issue of global asymptotic stabilization (GAS) for a group of linearly uncontrollable and unobservable time-delayed systems with uncertain control gains. As a result of the use of a nonsingular transformation and time rescaling, the group of nonlinear integrators with large delays are transformed into nonlinear integrators with small delays. Then, after applying both the homogeneous domination method and Lyapunov-Krasovskii (L-K) functionals, and revamping the adding a power integrator, we construct L-K functionals and a homogeneous non-smooth sampled-data controller, achieving GAS of the considered uncontrollable and unobservable time-delayed systems. Finally, an example is given to verify the efficiency of the proposed method.

中文翻译：

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通过采样数据控制实现一类时延系统的全局渐近稳定


本文讨论了一组线性不可控和不可观测的时滞系统的全局渐近稳定 （GAS） 问题，这些系统具有不确定的控制增益。由于使用了非奇异变换和时间重新缩放，具有大延迟的非线性积分器组被转换为具有小延迟的非线性积分器。然后，在应用齐次支配法和 Lyapunov-Krasovskii （L-K） 泛函后，并改进添加功率积分器，我们构建了 L-K 泛函和齐次非平滑采样数据控制器，实现了被认为不可控和不可观察的时滞系统的 GAS。最后，通过算例验证了所提方法的有效性。