Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 583947, 12 pages
Research Article

Guaranteed Performance Robust Kalman Filter for Continuous-Time Markovian Jump Nonlinear System with Uncertain Noise

Jin Zhu, Junhong Park, Kwan-Soo Lee, and Maksym Spiryagin

Department of Mechanical Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea

Received 29 January 2008; Accepted 13 July 2008

Academic Editor: Paulo Gonçalves

Copyright © 2008 Jin Zhu 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.


Robust Kalman filtering design for continuous-time Markovian jump nonlinear systems with uncertain noise was investigated. Because of complexity of Markovian jump systems, the statistical characteristics of system noise and observation noise are time-varying or unmeasurable instead of being stationary. In view of robust estimation, maximum admissible upper bound of the uncertainty to noise covariance matrix was given based on system state estimation performance. As long as the noise uncertainty is limited within this bound via noise control, the Kalman filter has robustness against noise uncertainty, and stability of dynamic systems can be ensured. It is proved by game theory that this design is a robust mini-max filter. A numerical example shows the validity of this design.