Optimal Robust Estimation for Linear Uncertain Systems with Single Delayed Measurement

Abstract This paper deals with the optimal robust estimation problem for linear uncertain systems with single delayed measurement. The optimal robust estimator is derived based on the reorganized innovation analysis approach. The calculation of the optimal robust estimator involves solving two Riccati difference equations of the same dimensions as that of the original systems and one Lyapunov equation. A numerical example is given to show the effectiveness of the proposed approach.

[1]  Arjan van der Schaft,et al.  Proceedings of the 30th IEEE Conference on Decision and Control , 1991 .

[2]  David Zhang,et al.  Hinfinity Fixed-lag smoothing for discrete linear time-varying systems , 2005, Autom..

[3]  Huanshui Zhang,et al.  H/sub /spl infin// fixed-lag smoothing for descriptor systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[5]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Bor-Sen Chen,et al.  Minimax robust deconvolution filters under stochastic parametric and noise uncertainties , 1994, IEEE Trans. Signal Process..

[7]  Daizhan Cheng,et al.  Optimal estimation for continuous-time systems with delayed measurements , 2006, IEEE Trans. Autom. Control..

[8]  Y.C. Soh,et al.  A reorganized innovation approach to linear estimation , 2004, IEEE Transactions on Automatic Control.

[9]  Michael V. Basin,et al.  Optimal control for linear systems with multiple time delays in control input , 2006, IEEE Transactions on Automatic Control.

[10]  Fan Wang,et al.  Robust Kalman filters for linear time-varying systems with stochastic parametric uncertainties , 2002, IEEE Trans. Signal Process..

[11]  Leonid Mirkin,et al.  H/sup /spl infin// control and estimation with preview-part I: matrix ARE solutions in continuous time , 2005, IEEE Transactions on Automatic Control.

[12]  Lihua Xie,et al.  Robust filtering under stochastic parametric uncertainties , 2004, Autom..

[13]  Duncan McFarlane,et al.  Robust state estimation for uncertain systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[14]  H. Kwakernaak,et al.  Optimal filtering in linear systems with time delays , 1967, IEEE Transactions on Automatic Control.

[15]  Lihua Xie,et al.  Design and analysis of discrete-time robust Kalman filters , 2002, Autom..

[16]  Hong Qiao,et al.  Robust filtering for bilinear uncertain stochastic discrete-time systems , 2002, IEEE Trans. Signal Process..

[17]  José Claudio Geromel,et al.  Optimal linear filtering under parameter uncertainty , 1999, IEEE Trans. Signal Process..