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Abstract and Applied Analysis
Volume 2011, Article ID 970978, 22 pages
Research Article

𝐻 Estimation for a Class of Lipschitz Nonlinear Discrete-Time Systems with Time Delay

School of Control Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan 250061, China

Received 27 December 2010; Accepted 18 May 2011

Academic Editor: Elena Braverman

Copyright © 2011 Huihong Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The issue of 𝐻 estimation for a class of Lipschitz nonlinear discrete-time systems with time delay and disturbance input is addressed. First, through integrating the 𝐻 filtering performance index with the Lipschitz conditions of the nonlinearity, the design of robust estimator is formulated as a positive minimum problem of indefinite quadratic form. Then, by introducing the Krein space model and applying innovation analysis approach, the minimum of the indefinite quadratic form is obtained in terms of innovation sequence. Finally, through guaranteeing the positivity of the minimum, a sufficient condition for the existence of the 𝐻 estimator is proposed and the estimator is derived in terms of Riccati-like difference equations. The proposed algorithm is proved to be effective by a numerical example.