Mathematical Problems in Engineering
Volume 2004 (2004), Issue 1, Pages 33-48

Optimal guaranteed cost filtering for Markovian jump discrete-time systems

Magdi S. Mahmoud1 and Peng Shi2

1College of Engineering, United Arab Emirates University, P.O. Box 17555, Al-Ain, United Arab Emirates
2School of Technology, University of Glamorgan, Pontypridd, CF37 1DL, Wales, UK

Received 20 August 2001; Revised 7 November 2003

Copyright © 2004 Magdi S. Mahmoud and Peng Shi. 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.


This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.