Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 583947, 12 pages
Guaranteed Performance Robust Kalman Filter for Continuous-Time
Markovian Jump Nonlinear System with Uncertain Noise
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
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
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.