On March 20, 2025, the 75th Zhi Xin Forum was held in Lecture Hall 117 at the Zhi Xin Building, which was jointly organized by the College of Electronic and Information Engineering and Shanghai Institute of Intelligent Science and Technology of Tongji University. Prof. Gang Feng from City University of Hong Kong, was invited to give a lecture on“Lyapunov Stability Theorems for Infinite-delayed Systems and Their Applications”, which was moderated by Prof. Hao Zhang.

Professor Feng presents several Lyapuov stability theorems for infinite-delayed systems and their applications. Those theorems are developed based on a general model of infinite-delayed systems and a newly proved key technical lemma. The stability results are more general than existing stability results, and the corresponding conditions are more easily satisfied than existing ones. These new Lyapunov theorems are then applied to the problems of stabilizing both time-in-variant and time-varying linear systems with distributed infinite input delays, and the corresponding stabilizing controllers are developed. A distinctive advantage of the Lyapunov based time domain method proposed over the existing frequency domain method is that the former can be adopted to deal with more general systems, such as time-varying linear systems or even nonlinear systems. Examples are provided to illustrate the effectiveness of the results.

After the report, Prof. Gang Feng had a cordial exchange and discussion with the participating teachers and students, and he also encouraged them to actively broaden their horizons, explore, discover and solve new scientific problems based on his own experience. This report further expanded the vision of our teachers and students and enhanced their understanding and knowledge of Lyapunov stability theorems for infinite-delayed systems and their applications.