Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation

We investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the existence of desired robust exponential filters, which are derived in terms of the solutions to algebraic Riccati inequalities. The developed theory is illustrated by numerical simulation.

[1]  Heinz Unbehauen,et al.  Robust state estimation for perturbed continuous systems with circular pole and error variance constraints , 1998 .

[2]  Pramod P. Khargonekar,et al.  FILTERING AND SMOOTHING IN AN H" SETTING , 1991 .

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

[4]  P. Belanger,et al.  Minimum-sensitivity filter for linear time-invariant stochastic systems with uncertain parameters , 1976 .

[5]  Uri Shaked,et al.  Robust H2 filtering for uncertain systems with measurable inputs , 1999, IEEE Trans. Signal Process..

[6]  Sérgio Ricardo de Souza,et al.  Output Feedback Stabilization of Uncertain Systems through a Min/Max Problem* , 1993 .

[7]  Uri Shaked,et al.  Robust minimum variance filtering , 1995, IEEE Trans. Signal Process..

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

[9]  Konrad Reif,et al.  The extended Kalman filter as an exponential observer for nonlinear systems , 1999, IEEE Trans. Signal Process..

[10]  U. Shaked,et al.  H/sub infinity /-optimal estimation: a tutorial , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[11]  Biao Huang,et al.  Robust H2/H∞ filtering for linear systems with error variance constraints , 2000, IEEE Trans. Signal Process..

[12]  Y. Hung,et al.  H ∞ Optimal control: Part 2. Solution for controllers , 1989 .

[13]  K. Grigoriadis,et al.  A Combined Alternating Projections and Semidefinite Programming Algorithm for Low-Order Control Design , 1996 .

[14]  M. Mahmoud,et al.  Robust Kalman filtering for continuous time-lag systems , 1999 .

[15]  Heinz Unbehauen,et al.  Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case , 1999, IEEE Trans. Autom. Control..

[16]  E. Yaz,et al.  Observer design for discrete and continuous non-linear stochastic systems , 1993 .

[17]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[18]  John O'Reilly,et al.  Observers for Linear Systems , 1983 .

[19]  Jean-Michel Dion,et al.  Stability and robust stability of time-delay systems: A guided tour , 1998 .

[20]  P. Khargonekar,et al.  Filtering and smoothing in an H/sup infinity / setting , 1991 .

[21]  Wei-Yong Yan,et al.  Design of low-order linear-phase IIR filters via orthogonal projection , 1999, IEEE Trans. Signal Process..

[22]  D. Bernstein,et al.  Steady-state kalman filtering with an H∞ error bound , 1989, 1989 American Control Conference.

[23]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[24]  F. Chorlton,et al.  Differential Equations and Applications , 1966 .

[25]  Zidong Wang.  Robust filter design with time-varying parameter uncertainty and error variance constraints , 1999 .

[26]  Lihua Xie,et al.  H∞ estimation for uncertain systems , 1992 .

[27]  Patrizio Colaneri,et al.  Finite escapes and convergence properties of guaranteed-cost robust filters , 1997, Autom..

[28]  E. Yaz.  On the almost sure and mean-square exponential convergence of some stochastic observers , 1990 .

[29]  U. Shaked,et al.  H,-OPTIMAL ESTIMATION: A TUTORIAL , 1992 .

[30]  G. Nicolao,et al.  Optimal robust filtering with time-varying parameter uncertainty , 1996 .

[31]  Shing-Tai Pan,et al.  Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems , 1996 .

[32]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[33]  D. Bernstein,et al.  Steady-state Kalman filtering with an H ∞ error bound , 1989 .

[34]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[35]  Heinz Unbehauen,et al.  Robust Hinfinity observer design of linear state delayed systems with parametric uncertainty: the discrete-time case , 1999, Autom..

[36]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[37]  Uri Shaked,et al.  H/sub infinity /-minimum error state estimation of linear stationary processes , 1990 .

[38]  Engin Yaz,et al.  Robust, exponentially fast state estimator for some non-linear stochastic systems , 1992 .

[39]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

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

[41]  X. Mao,et al.  Robustness of exponential stability of stochastic differential delay equations , 1996, IEEE Trans. Autom. Control..

[42]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..

[43]  Minyue Fu,et al.  Robust 𝒽∞ filtering for continuous time varying uncertain systems with deterministic input signals , 1995, IEEE Trans. Signal Process..