发表机构
Coordinated Science Laboratory, University of Illinois Urbana-Champaign; ASRI, Department of Electrical and Computer Engineering, Seoul National University（伊利诺伊大学厄巴纳-香槟分校协调科学实验室; 首尔国立大学电气与计算机工程系自动系统与鲁棒控制研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究慢-快非线性系统的稳定性，通过平均化构造平均系统，在慢变化总变差有界且快变化足够快时，证明系统状态保持在移动平衡邻域内，并用非线性切换系统实例验证。
AI 中文摘要
我们研究了同时受慢变和快变时间变化影响的非线性系统的稳定性。两者都可以具有不连续性，将切换系统作为特例涵盖在内。假设快变化是周期性的；因此，我们依赖平均化方法来构造一个平均系统。重要的是，平均系统的平衡依赖于慢变化，并假设当该慢输入被冻结时，该平衡是指数稳定的。利用扰动和李雅普诺夫分析，我们建立了一个实用稳定性结果，表明当慢变化的总变差（流动和跳跃）被适当界定且快输入变化足够快时，系统状态保持在移动平衡的邻域内。该结果通过一个具有慢-快切换和模式依赖平衡的非线性切换系统进行了说明。
英文摘要
We study the stability of nonlinear systems subject to both slow and fast time variations. Both can have discontinuities, covering switched systems as a special case. The fast variation is assumed to be periodic; thus, we rely on averaging to construct an average system. Importantly, the equilibrium of the average system depends on the slow variation and is assumed to be exponentially stable when this slow input is frozen. Using perturbation and Lyapunov analyses, we establish a practical stability result showing that the system state remains within a neighborhood of the moving equilibrium when the total variation (flows and jumps) of the slow variation is appropriately bounded and the fast input varies sufficiently fast. The result is illustrated via a nonlinear switched system with slow-fast switching and a mode-dependent equilibrium.
Comments65th IEEE Conference on Decision and Control (CDC), Honolulu, HI, USA, Dec. 2026
