Optimal filtering of discrete-time hybrid systems
Journal of Optimization Theory and Applications
Automatica (Journal of IFAC)
SIAM Journal on Control and Optimization
Brief paper: Detection and estimation for abruptly changing systems
Automatica (Journal of IFAC)
Brief H∞ control and filtering of discrete-time stochastic systems with multiplicative noise
Automatica (Journal of IFAC)
A new recursive filter for systems with multiplicative noise
IEEE Transactions on Information Theory
Observer-Based H∞ fuzzy control for T-S fuzzy neural networks with random data losses
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part II
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In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline.