Faculty Host: Professor Zhong-ping Jiang
Hybrid dynamical systems have attracted the attention of many researchers in recent years. Such systems are capable of exhibiting simultaneously continuous-time dynamics and discrete-time dynamics, and jump phenomena. They provide a natural framework for mathematical modeling of complex reactive systems in which physical processes interact with man-made automated environments. This talk will discuss some recent results on the stabilization of hybrid dynamical systems. Assuming certain properties of a convex linear combination of the nonlinear vector fields, some stabilizing switching rules are proposed. Stability analysis is performed in terms of two measures so that the results can unify several stability criteria, such as Lyapunov stability, partial stability, orbital stability, and stability of an invariant set.
Xinzhi Liu received the BSc degree in mathematics from Shandong Normal University, Jinan, China, in 1982, and the MSc and PhD degrees, all in applied mathematics, from University of Texas, Arlington, in 1987 and 1988, respectively. He was a Post-Doctoral Fellow at the University of Alberta, Edmonton, Alberta, Canada, from 1988 to 1990. He joined the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada, as an Assistant Professor in 1990, where he became an Associate Professor and a Full Professor in 1994 and 1997 respectively.
His research areas include systems analysis, stability theory, hybrid dynamical systems, impulsive control, chaos synchronization, artificial neural networks, and communication security. He is the author or coauthor of over 200 research articles and two research monographs and 10 edited books. He is the Chief Editor of the journal, DCDIS Series A: Mathematical Analysis, the Co-Chief Editor of the Journal, DCDIS Series B: Applications and Algorithms, and the Co-Chief Editor of the Journal of Nonlinear Systems and Applications. He served as General Chair for several international conferences on dynamical systems and applications.