H∞ filter design for nonlinear systems with quantised measurements in finite frequency domain. Issue 5 (4th April 2017)

• Record Type: Journal Article
• Authors: El Hellani, D.; El Hajjaji, A.; Ceschi, R.
• Is Part Of: International journal of systems science. Volume 48:Issue 5(2017)
• Page Start: 1048
• Page End: 1059
• Publication Date: 2017-04-04
• Subjects: Nonlinear systems -- Takagi–Sugeno model -- discrete-time systems -- H∞ filtering -- quantisation -- finite frequency domain -- Finsler's lemma -- linear matrix inequality (LMI); System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2016.1236421
• Languages: English
• ISSNs: 0020-7721

Abstract

ABSTRACT: This paper deals with the problem of finite frequency (FF) H ∞ full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi–Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency ℓ2 gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H ∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H ∞ performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H ∞ attenuation level can be obtained by our developed approach in comparison with another result in the literature.