A constructive tool of nonlinear control system design, the method of control Lyapunov functions (CLFs), has found numerous applications in stabilization problems for continuous-time, discrete-time, and hybrid systems. In this paper, we address the fundamental question: Given a CLF, corresponding to a continuous-time controller with some predefined (e.g., exponential) convergence rate, can the same convergence rate be provided by an event-triggered controller? Under certain assumptions, we give an affirmative answer to this question and show that the corresponding event-based controllers provide positive dwell times between consecutive events. Furthermore, we prove the existence of self-triggered and periodic event-triggered controllers, providing stabilization with a known convergence rate.

中文翻译：

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具有已知收敛率的李雅普诺夫事件触发稳定

非线性控制系统设计的一种建设性工具，控制李雅普诺夫函数 (CLF) 的方法，已在连续时间、离散时间和混合系统的稳定性问题中找到了许多应用。在本文中，我们解决了一个基本问题：给定一个 CLF，对应于具有一些预定义（例如，指数）收敛速度的连续时间控制器，事件触发的控制器能否提供相同的收敛速度？在某些假设下，我们对这个问题给出了肯定的答案，并表明相应的基于事件的控制器在连续事件之间提供正停留时间。此外，我们证明了自触发和周期性事件触发控制器的存在，以已知的收敛速度提供稳定性。