Robust Kalman filtering for jump continuous time-lag systems

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, delayless state estimator guarantee 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.