Switched Linear Control Systems: Standard Decomposition, Canonical Forms, And Feedback Stabilization

by Prof. Zhendong Sun, Hamilton Institute, NUI Maynooth, Co. Kildare.

 :  24 May 2005 (Tue)
 :  3:30pm - 4:30pm
Venue  :  Room 1504, 1/F (Lifts 25-26), HKUST

In this talk, I'll present my recent work on feedback design of switched linear control systems. Based on the recent controllability/observability criteria, a switched linear control system is decomposed into submodes with clear structural information. For single-input controllable switched systems, we propose a canonical form via coordinate and feedback transformations. A multi-input controllable switched system can be transformed into a single-input one by (nonregular) feedback reduction. Utilizing the canonical forms, we discuss in detail the feedback stabilizability of switched linear control systems. For systems in the controllability canonical form, a sufficient condition for quadratic stabilizability is given along with a design algorithm. For systems with uncontrollable mode, we also address the feedback stabilizability under mild conditions. These results extends the standard linear theory to switched systems. In other words, we successfully `recover' part of the core theory of linear systems for switched linear control systems. Finally, we reveal through a counterexample that controllability does not necessarily imply linear feedback stabilizability which indicates the complexity of the stabilizability problem.

Dr Sun Zhendong received his BS (1990) in Applied Mathematics from Chinese Ocean University, MSC(1993) in Cybernetics and operational research from Xiaman University and PhD in Control theory and applications from Beijing University of Aeronautics and Astronautics (1996). He worked as a postdoctor research fellow in Tsinghua University from 1996 to 1998, Associate Professor at BUAA from 1998 to 2002, Research Fellow at National University of Singapore from Feb 2000 to April 2001, Research fellow at University of New South Whale from Jan 2002 to Sept 2002, and Senior Research Fellow at National University of Ireland from Nov 2002 to present. His research interest lies in control and design for hybrid/switched systems, nonlinear control theory with applications to mechanical systems and sampled-data systems and multirate control.


*** All are Welcome ***