Abstract
This paper focuses on the problem of delay-range-dependent L 2–L ∞ filter design for stochastic systems with time-varying delay. The time delay varies in an interval. A delay-range-dependent sufficient condition is formulated in terms of linear matrix inequalities (LMIs), which guarantees the existence of a linear filter. The proposed filter ensures that the filtering error system is stochastically asymptotically stable and that its L 2–L ∞ performance satisfies a prescribed level. The corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Basin, A.A. Garcia, J.R. Gonzalez, Optimal filtering for linear systems with state and observation delays. Int. J. Robust Nonlinear Control 15, 859–871 (2005)
M. Basin, E. Sanchez, R.M. Zuniga, Optimal linear filtering for systems with multiple state and observation delays. Int. J. Innov. Comput. Inf. Control 3, 1309–1320 (2007)
M. Basin, J. Perez, D.C. Alvarez, Optimal filtering for linear systems over polynomial observations. Int. J. Innov. Comput. Inf. Control 4, 313–320 (2008)
D.S. Bernstein, W.M. Haddad, Steady-state Kalman filtering with an H ∞ error bound. Syst. Control. Lett. 12, 9–16 (1989)
E.K. Boukas, Stabilization of stochastic nonlinear hybrid systems. Int. J. Innov. Comput. Inf. Control 1, 131–141 (2005)
E.K. Boukas, N.F. Al-Muthairi, Delay-dependent stabilization of singular linear systems with delays. Int. J. Innov. Comput. Inf. Control 2, 283–291 (2006)
B. Chen, J. Lam, S. Xu, Memory state feedback guaranteed cost control for neutral delay systems. Int. J. Innov. Comput. Inf. Control 2, 293–303 (2006)
H. Gao, J. Lam, C. Wang, Robust energy-to-peak filter design for stochastic time-delay systems. Syst. Control. Lett. 55, 101–111 (2006)
H. Gao, C. Wang, Delay-dependent robust H ∞ and L 2–L ∞ filtering for a class of uncertain nonlinear time-delay systems. IEEE Trans. Automat. Contr. 48, 1661–1666 (2003)
L. Guo, H. Wang, Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters. IEEE Trans. Circuits Syst. I 52, 1644–1652 (2005)
L. Guo, H. Wang, Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises. IEEE Trans. Automat. Contr. 51, 695–700 (2006)
L. Guo, F. Yang, C. Feng, Multi-objective filtering for nonlinear time delay systems with non-zero initial conditions based on convex optimization. Circuits Syst. Signal Process. 25, 591–607 (2006)
Y. He, M. Wu, J.H. She, G.P. Liu, Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans. Automat. Contr. 49, 828–832 (2004)
Y. He, M. Wu, J.H. She, G.P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control. Lett. 51(1), 57–65 (2004)
Y. He, Q.G. Wang, C. Lin, An improved H ∞ filter design for systems with time-varying interval delay. IEEE Trans. Circuits Syst. II 53, 1235–1239 (2006)
Y. He, Q.G. Wang, C. Lin, M. Wu, Delay-range-dependent stability for systems with time-varying delay. Automatica 43, 371–376 (2007)
C. Lin, Q.G. Wang, T.H. Lee, A less conservative robust stability test for linear uncertain time-delay systems. IEEE Trans. Automat. Contr. 51, 87–91 (2006)
M. Mahmoud, Robust Control and Filtering for Time-Delay Systems (Dekker, New York, 2000)
X. Mao, N. Koroleva, A. Rodkina, Robust stability of uncertain stochastic differential delay equations. Syst. Control. Lett. 35, 325–336 (1998)
J.H. Park, C.L. Chen, Guaranteed cost control of time-delay chaotic systems. Chaos Solitons Fractals 27, 1011–1018 (2006)
P. Shi, Robust filtering for uncertain delay systems under sampled measurements. Signal Process. 58, 131–151 (1997)
P. Shi, M. Mahmoud, S.K. Nguang, A. Ismail, Robust filtering for jumping systems with mode-dependent delays. Signal Process. 86, 140–152 (2006)
Z. Wang, K.J. Burnham, Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation. IEEE Trans. Signal Process. 49, 794–804 (2001)
Z. Wang, F. Yang, D.W.C. Ho, X. Liu, Robust H ∞ filtering for stochastic time-delay systems with missing measurements. IEEE Trans. Signal Process. 54, 2579–2587 (2006)
L. Wu, P. Shi, H. Gao, C. Wang, A new approach to robust H ∞ filtering for uncertain systems with both discrete and distributed delays. Circuits Syst. Signal Process. 26, 229–248 (2007)
J. Xia, S. Xu, B. Song, Delay-dependent L 2–L ∞ filter design for stochastic time-delay systems. Syst. Control. Lett. 56, 579–587 (2007)
S. Xu, T. Chen, Robust H ∞ filtering for uncertain impulsive stochastic systems under sampled measurements. Automatica 39, 509–516 (2003)
S. Xu, J. Lam, Improved delay-dependent stability criteria for time-delay systems. IEEE Trans. Automat. Contr. 50, 384–387 (2005)
B. Zhang, S. Xu, Robust L 2–L ∞ filtering for uncertain nonlinearly parameterized stochastic systems with time-varying delays. Circuits Syst. Signal Process. 26, 751–772 (2007)
B. Zhang, S. Xu, G. Zong, Y. Zou, Delay-dependent stabilization for stochastic fuzzy systems with time delays. Fuzzy Sets Syst. 158, 2238–2250 (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is partially supported by the Natural Science Foundation of China (60674055, 60774047), and the Taishan Scholar Programme of Shandong Province.
Rights and permissions
About this article
Cite this article
Zhou, Q., Chen, B., Li, H. et al. Delay-Range-Dependent L 2–L ∞ Filtering for Stochastic Systems with Time-Varying Interval Delay. Circuits Syst Signal Process 28, 331–348 (2009). https://doi.org/10.1007/s00034-008-9078-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-008-9078-z