Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 483568, 12 pages
Research Article

Finite-Horizon Optimal Control of Discrete-Time Switched Linear Systems

Qixin Zhu1,2,3 and Guangming Xie1,2

1The Center for System and Control, College of Engineering, Peking University, Beijing 100871, China
2School of Electrical and Electronic Engineering, East China Jiaotong University, Nanchang 330013, China
3Department of Mechanical and Electrical Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received 1 May 2012; Revised 2 July 2012; Accepted 10 July 2012

Academic Editor: Soohee Han

Copyright © 2012 Qixin Zhu and Guangming Xie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.