ABSTRACT
This paper is to investigate the linear minimum mean square error estimation for Markovian jump linear system subject to unknown Markov chains, multi-channel mode and observation delays, and packet losses. The reorganisation method is employed to convert the delayed measurement system into an equivalent delay-free one and a new state variable is introduced, by which the original state estimation with transmission delays and data losses is transformed into the new state estimation for the reorganised delay-free system with jumping parameters and multiplicative noises. The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations. Then the original state estimation will be obtained via the jumping property. Finally, we show that the difference Riccati equations converge to a set of generalised algebraic Riccati equations under appropriate assumptions, which result in an optimal stationary filter.
Acknowledgements
The authors are grateful to anonymous referees for their suggestions which have greatly improved the presentation of the paper.
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No potential conflict of interest was reported by the authors.
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Chunyan Han
Chunhan Han received her Ph.D. degree in Control Theory and Control Engineering from Shandong University in 2010. She is currently an associate professor at the School of Electrical Engineering, University of Jinan. Her research interest covers optimal control and estimation, time delay systems, and Markov jump linear systems.
Wei Wang
Wei Wang received his PhD degree in control science and engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently an associate professor at Shandong University. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.