报告题目：Switched Nonlinear Systems: Stability Analysis via Average Dwell Time and Average Activation Time Switching
报告人简介：Shenyu Liu（刘沈豫） is an assistant professor at the School of Automation, Beijing Institute of Technology (BIT), China. He received his B. Eng. degree in Mechanical Engineering and B.S. degree in Mathematics from the National University of Singapore in 2014. He obtained his M.S. degree in Mechanical Engineering at the University of Illinois at Urbana-Champaign in 2015 and completed his Ph.D. in Electrical and Computer Engineering in 2020 at the same institution. Before joining BIT, Dr. Liu worked as a postdoctoral researcher in the Department of Mechanical and Aerospace Engineering at the University of California, San Diego. His research interests include stability theory of switched/hybrid systems, Lyapunov methods for nonlinear systems, matrix perturbation theory, uncertain systems, and data-driven controller design.
报告内容简介：Switched nonlinear systems, characterized by dynamical subsystems controlled by a switching signal, provide a framework to model systems with transitions of dynamics. This talk investigates deterministic and stochastic stability properties, focusing on average dwell time (ADT) and average activation time (AAT) switching. For deterministic stability, we propose conditions on the switching frequency and activation time to guarantee global asymptotic stability, input-to-state stability, or integral-input-to-state stability. We present examples of switched nonlinear systems that exhibit instability under slowly switching signals satisfying the ADT condition. Consequently, we provide weaker characterizations and propose a generalized class of switching signals with an ADT/AAT-mixed condition to ensure stability. In the stochastic stability analysis, we contrast various stability properties of randomly switched systems. We propose a novel stability criterion for asymptotic mean stability based on a multi-mode renewal equation. For Markovian and semi-Markovian switched systems, we establish connections between asymptotic moment stability and the Hurwitzness of a matrix or the convergence of a solution of an auxiliary time-delayed system. These stability properties are closely related to the expected ADT and AAT conditions imposed on the switching signal.