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Mathematical Problems in Engineering
Volume 2014, Article ID 512485, 9 pages
Research Article

Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

1School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2School of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China

Received 16 April 2014; Revised 19 June 2014; Accepted 4 July 2014; Published 24 July 2014

Academic Editor: Xi-Ming Sun

Copyright © 2014 Lin Du et al. 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.


The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.