filter design for nonlinear systems with quantised measurements in finite frequency domain

D. El Hellani, A. El Hajjaji and R. Ceschi

International Journal of Systems Science, 2017, vol. 48, issue 5, 1048-1059

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.

Date: 2017
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DOI: 10.1080/00207721.2016.1236421

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