论文标题
离散时间自主系统的确定性和随机固定时间稳定性
Deterministic and Stochastic Fixed-time Stability of Discrete-time Autonomous Systems
论文作者
论文摘要
本文研究了自动非线性离散时间（DT）系统的确定性和随机固定时间稳定性。首先提出了Lyapunov条件，确定性DT系统的固定时间稳定性得到了认证。然后考虑确定性扰动和随机噪声下的系统扩展。对于前者，分析了对固定时间稳定DT系统扰动的敏感性，并表明固定时间吸引力是由提出的Lyapunov条件引起的。对于后者，提出了足够的Lyapunov条件，以实现非线性随机DT系统概率的固定时间稳定性。定居时间函数的固定上限是针对固定时稳定和固定时间有吸引力的系统得出的，并且随机DT系统得出了随机沉降时函数固定上限。给出了说明性示例以及仿真结果，以验证引入的结果。
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified. Extensions to systems under deterministic perturbations as well as stochastic noise are then considered. For the former, the sensitivity to perturbations for fixed-time stable DT systems is analyzed, and it is shown that fixed-time attractiveness is resulted from the presented Lyapunov conditions. For the latter, sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented. The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems, and the stochastic settling-time function fixed upper bound is derived for stochastic DT systems. Illustrative examples are given along with simulation results to verify the introduced results.
