离散自治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
摘要：
本文研究自治非线性离散时间系统的确定性和随机固定时间稳定性。首先给出了确定性DT系统的固定时间稳定性的李雅普诺夫条件。扩展到确定性扰动以及随机噪声下的系统，然后考虑。对于前者，分析了固定时间稳定DT系统对扰动的敏感性，并证明了固定时间吸引性是由所给出的李雅普诺夫条件引起的。对于后者，给出了非线性随机DT系统定时概率稳定的充分李雅普诺夫条件。对于固定时间稳定系统和固定时间吸引系统，给出了稳定时间函数的固定上界;对于随机DT系统，给出了稳定时间函数的随机上界。给出了说明性的例子以及仿真结果来验证所介绍的结果。
英文摘要：
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.
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