Using a new implicit discretization scheme, we study in this paper the existence and uniqueness of strong solutions for a class of Lur'e dynamical systems where the set-valued feedback depends on both time and state. This work is a generalization of \cite{abc} where the time-dependent set-valued feedback is considered to acquire only weak solutions. Obviously, strong solutions and implicit discretization scheme are nice properties, especially for numerical simulation. We also provide some conditions such that the solutions are exponentially attractive. The obtained results can be used to study the time-varying Lur'e systems with errors in data. Our result is new even the set-valued feedback depends only on the time.
Regularized Model Predictive Control via Contractivity and Implicit Lur'e Analysis
Toyota Central Research and Development Laboratories, Incorporated（丰田中央研究所）；Center for Control, Dynamical Systems, and Computation, UC Santa Barbara（加州大学圣塔芭芭拉分校控制、动力学与计算中心）；Department of Mechanical Engineering, Rice University（莱斯大学机械工程系）
Existence of Relaxed Equilibrium for Time-Inconsistent Mean Field Games: A Set-Valued Fixed Point Approach
Zhongtai Securities Institute for Financial Studies, Shandong University（山东大学中泰金融研究院）；School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）
A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization
Zhejiang University（浙江大学）；National University of Singapore（新加坡国立大学）；Huzhou Normal University（湖州师范学院）；State Key Laboratory of Industrial Control Technology, the Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University（浙江大学控制科学与工程学院网络控制系统研究所工业控制技术国家重点实验室）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）
