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Quantized H ∞ filtering for state‐delayed systems with finite frequency specifications
Author(s) -
El Hellani D.,
El Hajjaji A.,
Ceschi R.
Publication year - 2018
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2896
Subject(s) - control theory (sociology) , lemma (botany) , mathematics , filter (signal processing) , frequency domain , stability (learning theory) , range (aeronautics) , state (computer science) , filter design , linear matrix inequality , computer science , algorithm , mathematical optimization , mathematical analysis , engineering , ecology , control (management) , poaceae , artificial intelligence , machine learning , computer vision , biology , aerospace engineering
Summary This paper presents a novel design approach for the finite frequency (FF) H ∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ℓ 2 gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ℓ 2 gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.