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Robust filtering under randomly varying sensor delay with variance constraints
Copyright [2004] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper deals with a new filtering problem for linear uncertain discrete-time stochastic systems with randomly varying sensor delay. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. The system measurements are subject to randomly varying sensor delays, which often occur in information transmissions through networks. The problem addressed is the design of a linear filter such that, for all admissible parameter uncertainties and all probabilistic sensor delays, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. We show that the filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. We also characterize the set of desired robust filters in terms of some free parameters. An illustrative numerical example is used to demonstrate the usefulness and flexibility of the proposed design approach
Variance-constrained filtering for uncertain stochastic systems with missing measurements
Copyright [2003] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach
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