Abstract
In this paper, a new robust H ∞ filtering problem for uncertain time-delay systems is considered. Based on the Lyapunov method, a design criterion of the robust H ∞ filter, in which the filtering process remains asymptotically stable for all admissible uncertainties and the transfer function from the disturbance inputs to error state outputs satisfies the prespecified H ∞ norm upper bound constraint, is derived in terms of matrix inequalities. The inequalities can be solved easily by efficient convex optimization algorithms. A numerical example is included to illustrate the validity of the proposed design approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Leitmann, G., On One Approach to the Control of Uncertain Systems, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 373–380, 1993.
Leitmann, G., Udwadia, F. E., and Kryzahimskii, A. V., Editors, Dynamics and Control, Gordon and Breach, Amsterdam, Holland, 1999.
Udwadia, F. E., Weber, H. I., and Leitmann, G., Editors, Dynamical Systems and Control, CRC Press, New York, NY, 2004.
Hale, J., and Verduyn Lunel, S. M., Introduction to Functional Differential Equations, Springer Verlag, New York, NY, 1993.
Niculescu, S. I., Delay Effects on Stability: A Robust Approach, Lecture Notes in Control and Information Sciences, Springer, New York, NY, Vol. 269, 2002.
Park, J.H., Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties, Journal of Optimization Theory and Applications, Vol. 108, pp. 155–174, 2001.
Kwon, O., and Park, J.H., On Improved Delay-Dependent Robust Control for Uncertain Time-Delay Systems, IEEE Transactions on Automatic Control, Vol. 49, pp. 1991–1995, 2004.
Li, H., and Fu, M., A Linear Matrix Inequality Approach to Robust mathcalH_∞ Filtering, IEEE Transactions on Signal Processing, Vol. 45, pp. 2338–2350, 1997.
Palhares, R.M., and Peres, P.L., Robust H_∞ Filtering Design with Pole Placement Constraint via Linear Matrix Inequalities, Journal of Optimization Theory and Applications, Vol. 102, pp. 239–261, 1999.
Park, J. H., Kwon, O., Lee, S., and Won, S., On Robust H_∞ Filter Design for Uncertain Neutral Systems: LMI Optimization Approach, Applied Mathematics and Computation, Vol.159, pp. 625–639, 2004.
De Souza, C. E., Palhares, R. M., and Peres, P. L. D., Robust mathcalH_∞ Filter Design for Uncertain Linear Systems with Multiple Time-Varying State Delays, IEEE Transactions on Signal Processing, Vol. 49, pp. 569–576, 2001.
Xu S., and Chen T., An LMI Approach to the H ∞ Filter Design for Uncertain Systems with Distributed Delays, IEEE Transactions on Circuits and Systems-II: Express Briefs, Vol. 51, pp. 195–201, 2004.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory, Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, Vol. 15, 1994.
Gu, K., An Integral Inequality in the Stability Problem of Time-Delay Systems, Proceedings of the IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810, 2000.
Yue, D., and Won, S., Delay-Dependent Robust Stability of Stochastic Systems with Time Delay and Nonlinear Uncertainties, Electronics Letters, Vol. 37, pp. 992–993, 2001.
Gahinet, P., Nemirovski, A., Laub, A., and Chilali, M., LMI Control Toolbox User&s Guide. The Mathworks, Natick, Massachusetts, 1995.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
Rights and permissions
About this article
Cite this article
Kwon, O.M., Park, J.H. Robust H ∞ Filtering for Uncertain Time-Delay Systems: Matrix Inequality Approach. J Optim Theory Appl 129, 309–324 (2006). https://doi.org/10.1007/s10957-006-9064-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-006-9064-1