Delay-dependent filtering for discrete-time state-delayed systems with small gain conditions in finite frequency ranges

• Published in: International journal of adaptive control and signal processing Vol. 25; no. 11; pp. 983 - 1005
• Main Authors: Zhang, Xiao-Ni, Yang, Guang-Hong
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.11.2011
• Subjects: delay-dependent filtering; discrete-time; Filtering; Filtration; finite frequency range; Frequency ranges; Gain; Mathematical analysis; Mathematical models; Signal processing; small gain condition; state-delayed system; Synthesis
• ISSN: 0890-6327; 1099-1115; 1099-1115
• DOI: 10.1002/acs.1253

This paper is concerned with the delay‐dependent filtering problem for linear discrete‐time multi‐delay systems with small gain conditions in finite frequency ranges. A new multiplier method is developed to convert the resulting nonconvex filtering synthesis conditions to the ones based on linear matrix inequalities (LMIs). Thus, sufficient conditions for the existence of feasible filters are given in terms of solutions to a set of LMIs. For the entire frequency case, it is shown that the proposed result is less conservative than the relative existing results. Finally, the procedures and the advantages of the proposed approach in comparison with the existing ones in the entire frequency range are illustrated via numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.