报告人：Cheng-Zhong Xu

报告人简介：Cheng-Zhong Xu received the master degree in automatic control in 1983 from China University of Petroleum (East China), the PhD degree in automatic control and signal processing in 1989 from Institut National Polytechnique de Grenoble, France, and the Habilitation degree in applied mathematics and automatic control in 1997 from University of Metz. From 1991 through 2002 he was chargé de recherche (research officer) in INRIA (Institut National de Recherche en Informatique et en Automatique). Since 2002 he has been a professor of automatic control in University of Lyon, France. He has taught the control theory of linear feedback systems and robust control for master students. His research interests include control of distributed parameter systems (described by partial differential equations), numerical simulations of PDE systems and its applications to mechanical and chemical engineering. He has supervised numerous PhD students in the field of observation and stabilization of infinite-dimensional vibrating systems. From 1995 through 1998 he was an associated editor of the IEEE Transactions on Automatic Control. Currently he is associated editor of the SIAM Journal on Control and Optimization.

摘要：The talk is concerned with the control of a fluid flow system governed by nonlinear hyperbolic partial differential equations. Both the control and the output observation are located on the boundary.We study local stability of the equilibrium states by using Lyapunov approach. We present a strict Lyapunov function for time-invariant hyperbolic systems and establish a necessary and sufficient condition for exponential stability of the null equilibrium state. Using the necessary and sufficient condition we prove that the linearized flow system is exponentially stable around each subcritical hydraulic equilibrium state. A systematic design of PI (proportional and integral) controllers is proposed for the flow system based on the linearized model. Robust stabilization of the closed-loop nonlinear system by the designed PI controller is proved by using the direct Lyapunov method.