An LMI approach to the H∞ filter design for uncertain systems with distributed delays

This paper investigates the problem of robust H/sub /spl infin// filter design for linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both the state and measurement equations. The problem we address is the design of a filter, such that for all admissible uncertainties, the resulting error system is asymptotically stable and satisfies a prescribed H/sub /spl infin// performance level. A sufficient condition is obtained to guarantee the existence of desired H/sub /spl infin// filters, which can be constructed by solving certain linear matrix inequalities. The effectiveness of the proposed design method is demonstrated by a numerical example.

[1]  A. E. Pearson,et al.  A multistage reduction technique for feedback stabilizing distributed time-lag systems , 1987, Autom..

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

[3]  C. D. Souza,et al.  H∞ Filtering for Continuous-Time Linear Systems with Delay , 1996 .

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

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

[6]  Shengyuan Xu,et al.  Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty , 2002 .

[7]  Kok Lay Teo,et al.  Envelope-constrained IIR filter design via H/sub /spl infin// optimization methods , 1999 .

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

[9]  L. Crocco.  Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part I: Fundamentals. Low Frequency Instability With Monopropellants , 1951 .

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

[11]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[12]  Jean-Pierre Richard,et al.  Stability of some linear systems with delays , 1999, IEEE Trans. Autom. Control..

[13]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for stochastic systems , 2002, IEEE Trans. Signal Process..

[14]  Lihua Xie,et al.  Envelope-Constrained FIR Filter Design , 2000 .

[15]  Lihua Xie,et al.  Envelope-constrained H/sub /spl infin// FIR filter design , 2000 .

[16]  Shengyuan Xu.  Robust H/sub /spl infin// filtering for a class of discrete-time uncertain nonlinear systems with state delay , 2002 .

[17]  O. Sename,et al.  H/sub /spl infin// observer design for time-delay systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[18]  Mauro Olivieri,et al.  Design and characterization of a standard cell set for delay insensitive VLSI design , 1994 .