Stability Analysis of Infinite-dimensional Event-triggered and Self-triggered Control Systems with Lipschitz Perturbations
Stability Analysis of Infinite-dimensional Event-triggered and Self-triggered Control Systems with Lipschitz Perturbations
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DOI：
10.3934/mcrf.2021021
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发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
M. Wakaiki;H. Sano
中科院分区：
文献类型：
--
作者：
M. Wakaiki;H. Sano
本文解决了以下问题：“假设状态反馈控制器稳定了无限维线性连续时间系统。如果我们适当地选择事件/自触发机制的参数，事件/自触发控制系统在所有足够小的非线性 Lipschitz 扰动下是否稳定？”我们假设稳定反馈算子是紧凑的。该假设用于保证事件间时间的严格正性以及具有无界控制算子的演化方程的温和解的存在性。首先，对于控制算子有界的情况，我们证明上述问题的答案是肯定的，给出了指数稳定性的充分条件，可用于事件/自触发机制的设计。接下来，我们研究控制算子无界的情况，并证明对于周期性事件触发机制，答案仍然是肯定的。
This paper addresses the following question: ``Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuous-time system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the event/self-triggered control system stable under all sufficiently small nonlinear Lipschitz perturbations?'' We assume that the stabilizing feedback operator is compact. This assumption is used to guarantee the strict positiveness of inter-event times and the existence of the mild solution of evolution equations with unbounded control operators. First, for the case where the control operator is bounded, we show that the answer to the above question is positive, giving a sufficient condition for exponential stability, which can be employed for the design of event/self-triggering mechanisms. Next, we investigate the case where the control operator is unbounded and prove that the answer is still positive for periodic event-triggering mechanisms.