On H∞ Filtering for a Class of Uncertain Nonlinear Neutral Systems

AbstractThis paper investigates the problem of robust H∞ filtering for a class of nonlinear neutral systems with norm-bounded parameter uncertainties appearing in all the matrices of the linear part of the system model. The nonlinearities are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear filter that guarantees both the robust stability and a prescribed H∞ performance of the filtering error dynamics irrespective of the parameter uncertainties. A sufficient condition for the solvability of this problem is given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expression of a desired H∞ filter is also presented. A numerical example is provided to demonstrate the effectiveness of the proposed approach.

[1]  Pedro Luis Dias Peres,et al.  Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays , 2001, IEEE Trans. Signal Process..

[2]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[3]  R. Rajamani,et al.  Existence and design of observers for nonlinear systems: Relation to distance to unobservability , 1998 .

[4]  Shengyuan Xu,et al.  H∞ and positive-real control for linear neutral delay systems , 2001, IEEE Trans. Autom. Control..

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

[6]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[7]  Jong Hae Kim,et al.  H∞-output feedback controller design for linear systems with time-varying delayed state , 1998, IEEE Trans. Autom. Control..

[8]  Uri Shaked,et al.  𝒽∞ Filtering for Continuous-time Linear Systems with Delay , 1999, IEEE Trans. Autom. Control..

[9]  Anas Fattouh,et al.  H, Observer Design for Time-Delay Systems , 1998 .

[10]  Shengyuan Xu,et al.  An LMI approach to guaranteed cost control for uncertain linear neutral delay systems , 2003 .

[11]  J. Hale.  Theory of Functional Differential Equations , 1977 .

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

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

[14]  Emilia Fridman,et al.  A new H∞ filter design for linear time delay systems , 2001, IEEE Trans. Signal Process..

[15]  Lihua Xie,et al.  Robust filtering for a class of discrete-time uncertain nonlinear systems: AnH∞ approach , 1996 .

[16]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[17]  R. Brayton.  Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type , 1966 .

[18]  Lihua Xie,et al.  On robust filtering for linear systems with parameter uncertainty , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[19]  Shengyuan Xu,et al.  Robust Filtering for a Class of Discrete-Time Uncertain Nonlinear Systems with State Delay , 2002 .

[20]  Lihua Xie,et al.  H ∞ filtering for a class of uncertain nonlinear systems , 1993 .

[21]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[22]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain impulsive stochastic systems under sampled measurements , 2003, Autom..