Mahmoud, Magdi S and Shi, Peng (2003) Robust Kalman Filtering for Continuous Time-Lag Systems With Markovian Jump Parameters. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Circuits and Systems, 50 (1). pp. 98-105. ISSN 1057-7122

Abstract

The problem of continuous-time Kalman filtering for a class of linear, uncertain time-lag systems with randomly jumping parameters is considered. The parameter uncertainties are norm bounded and the transitions of the jumping parameters are governed by a finite-state Markov process. We establish LMI-based sufficient conditions for stochastic stability. The conditions under which a linear delay-less state estimator guarantees that the estimation error covariance lies within a prescribed bound for all admissible uncertainties are investigated. It is established that a robust Kalman filter algorithm can be determined in terms of two Riccati equations involving scalar parameters. The developed theory is illustrated by a numerical example.

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