论文标题
多项式稳定性相对于采样
Robustness of Polynomial Stability with Respect to Sampling
论文作者
论文摘要
我们对以下关于采样的多项式稳定性的鲁棒性提供了部分肯定的答案：我们将理想的采样器和零级保持量应用于控制器周围的反馈循环。那么，对所有足够小的采样期的采样数据系统是否稳定稳定？此外，在足够快速的采样下，连续时间系统的多项式衰减是否转移到采样数据系统？我们提供了在快速采样下保留强稳定性的条件。此外，我们估计采样数据系统状态的衰减速率具有光滑的初始状态和足够小的采样期。
We provide a partially affirmative answer to the following question on robustness of polynomial stability with respect to sampling: ``Suppose that a continuous-time state-feedback controller achieves the polynomial stability of the infinite-dimensional linear system. We apply an idealized sampler and a zero-order hold to a feedback loop around the controller. Then, is the sampled-data system strongly stable for all sufficiently small sampling periods? Furthermore, is the polynomial decay of the continuous-time system transferred to the sampled-data system under sufficiently fast sampling?'' The generator of the open-loop system is assumed to be a Riesz-spectral operator whose eigenvalues are not on the imaginary axis but may approach it asymptotically. We provide conditions for strong stability to be preserved under fast sampling. Moreover, we estimate the decay rate of the state of the sampled-data system with a smooth initial state and a sufficiently small sampling period.
