Mathematical Problems in Engineering 
Volume 2004 (2004), Issue 1, Pages 33-48
doi:10.1155/S1024123X04108016

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

Abstract

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.