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{H}_{\infty } Filtering for Discrete-Time State-Delayed Systems With Finite Frequency Specifications

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2 Author(s)
Huijun Gao ; Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, China ; Xianwei Li

This article researches the problem of finite frequency (FF) H filtering for linear discrete-time state-delayed systems. The disturbance is assumed to reside in low/middle/high frequency ranges. To reduce the conservatism of the results, delay-partitioning idea is used to derive a new FF bounded real lemma (BRL). By applying the generalized Kalman-Yakubovich-Popov lemma, two equivalent approaches to the proof of the proposed FF BRL are given, respectively, starting from transfer function and Lyapunov-Krasovskii functional. A new FF H filter design method is proposed in terms of solving a set of linear matrix inequalities. Finally, a numerical example clearly demonstrates the merits and effectiveness of the proposed method.

Published in:

IEEE Transactions on Automatic Control  (Volume:56 ,  Issue: 12 )