Fundamental Theory of Controllability and Observability of First-Order Matrix Difference Systems


 

Professor Yan Wu
Department of Mathematical Sciences
Georgia Southern University
P.O. Box 8093
Statesboro, GA 30460-8093
USA
E-mail: yan@georgiasouthern.edu

Abstract: The theory of difference equations is much wealthier than its counterpart in differential equations. With the emergence of digital signal processing technology, the theory of difference equations assumes great importance in areas such as digital control, image processing, and digital filter design. In this talk, a first-order matrix Sylvester difference system with a control structure is discussed in view of the existence and uniqueness of its general solution. Results are used in the study of controllability and observability of the matrix difference system coupled with an output structure. More general criteria, such as the one-sided controllability and observability matrices, are obtained for complete controllability and complete observability of time-invariant systems.

Brief Biography of the Speaker:
Yan Wu received the B.S. degree in Mathematics from Beijing University of Technology in 1992, and the Ph.D. degree in Applied Mathematics and Electrical Engineering both from University of Akron in 1996 and 2000, respectively.

Currently he is an Associate Professor in the Department of Mathematical Sciences at Georgia Southern University. His research interests include numerical linear algebra, nonlinear control, and generalized sampling theory. He has two patents granted by the United States Patent and Trademark Office. One of his papers was ranked 4th place among the top 25 publications in the Journal of Digital Signal Processing in 2006. Dr. Wu serves as an Associate Editor for Instrumentation, Systems, and Automation (ISA) and American Automatic Control Council (AACC).