Study Of Robust H_∞ Filtering In Parameter Uncertainty Linear System Based On LMI

In classical minimum variance filtering, it is implicitly assumed that the signal models are exactly known and the noise sources are stationary white noise signals with known statistics. Unfortunately, these assumptions limit the application of minimum variance estimators as in many situations, only an approximate signal model is available and the statistics of the noise sources are not fully known or unavailable. To handle the above problem, an alternative approach called H_∞filtering has been introduced. In H_∞filtering the noise signals are assumed to be arbitrary signals with bounded energy and the problem is to design an estimator which ensures a bound on the H_∞-norm of the transfer function from the noise signals to the estimation error. Although it is known to be more robust than the corresponding Kalman filter with respect to noise signals uncertainty, the standard H_∞filtering fails to provide a guaranteed performance when the system model is subject to parametric uncertainty. A robust H_∞filtering methodology has been developed for linear systems subjected to norm-bounded parameter uncertainty. The objective is to design a filter such that the H_∞-norm of the operator from the noise signals to the estimation error is guaranteed to be within a prescribed bound for all admissible uncertainties.With the successful application of linear matrix inequality of the research of robust control, many internal and oversea scholars intend to transform the robust filtering of uncertain systems into solving the problems of LMI. This thesis deals with the problem of robust H_∞filter for linear systems with norm-bounded parameter uncertainty in all the matrices of the system state-space model, including the coefficient matrices of the noise signal. This thesis sets its focus on the state space models with parameter uncertainty in state matrix and noise disturbance matrix. Using LMI method, this thesis presents the simple test condition of robust H_∞filter and robust H_∞cost guaranteed filter in the form of LMI. The solver feasp in LMI toolbox can testify the feasibility of this LMI and presents the feasible solution in case it is feasible. The parameters of the filter can then be easily deduced. Further more, the solver mincx of LMI toolbox can be used to solve the convex optimization with LMI and linear objective function constraints. The yield will be an optimal filter for the system. At last, with the state space model discussed in this thesis, a simulation is carried through on the new kind of LMI and the results are compared. The effectiveness of the method is thus proved.