存在大未知延迟时含幂零矩阵系统的固定时间镇定
Fixed-time stabilization of systems with nilpotent matrices in the presence of large unknown delays
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中文总结 AI 辅助
研究含幂零矩阵且有大未知延迟的线性系统的固定时间镇定问题，通过引入人工延迟设计反馈，能在固定时间使状态归零并实现输入到状态稳定，该方法可用于扰动单积分器及时延系统，数值模拟验证了有效性。
中文摘要 AI 辅助
本文研究存在具有已知界限的未知大常数输入/测量延迟时，含幂零矩阵的连续时间扰动线性系统的状态反馈固定时间镇定。通过使用额外的人工延迟，设计一种反馈，对于具有幂零矩阵的精确已知线性系统，能在固定时间（大于未知延迟界限）将状态驱动至零，在存在加性干扰、小系统矩阵扰动和非线性时实现具有大指数衰减率的输入到状态稳定性。对于扰动单积分器，在存在具有已知界限的快速变化未知测量延迟时实现固定时间镇定。结果扩展到离散时间系统。数值模拟说明了结果的有效性。
英文摘要
In this paper, we study state-feedback fixed-time stabilization of continuous-time perturbed linear systems with nilpotent matrices in the presence of unknown large constant input/measurement delays with known bounds. By using an additional artificial delay, we design a feedback that for a precisely known linear system with a nilpotent matrix drives the state to zero in fixed time (which is larger than the bound of the unknown delay) and achieves input-to-state stability with a large exponential decay rate in the presence of additive disturbances and small system matrix perturbations and nonlinearities. For perturbed single integrators, fixed-time stabilization is achieved in the case of fast-varying unknown measurement delays with known bounds. The results are extended to discrete-time systems. Numerical simulations illustrate the efficiency of the results.
