IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 2003 · 155 citations · 17 references
Natural SciencesMathematicsSystems EngineeringDynamical SystemsStochastic ProcessesUncertainty QuantificationControl TheoryKalman FilteringStability TheoryState EstimationStochastic ControlStochastic StabilityContinuous-time Dynamical SystemsContinuous-time Kalman FilterFinite-state Markov ChainsLinear State EstimationMarkov Jump SystemsRobust Control Of Time-varying SystemsRobust Kalman FilterRobust Stochastic Stability
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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Brian D. O. Anderson, J.B. Moore, Mansour Eslami · IEEE Transactions on Systems Man and Cybernetics · 1982 · 3.2K citations
Stochastic stability properties of jump linear systems
Xiangbo Feng, Kenneth A. Loparo, Y. Ji et al. · IEEE Transactions on Automatic Control · 1992 · 724 citations
Brian D. O. Anderson, J.B. Moore, Mansour Eslami · IEEE Transactions on Systems Man and Cybernetics · 1982 · 447 citations