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

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.

KEYWORDS:

• Nonlinear systems
• Takagi–Sugeno model
• discrete-time systems
• H_∞ filtering
• quantisation
• finite frequency domain
• Finsler's lemma
• linear matrix inequality (LMI)

Disclosure statement

No potentialconflict of interest was reported by the authors.

Additional information

Notes on contributors

D. El Hellani

Doha El Hellani received the degree of electrical and Electronic Engineering from the Lebanese University, and her master degree in Industrial Control from both the Lebanese University and the University of Technology (Compiegne, France) in 2013. Since 2014, she has joined the University of Picardie Jules Verne (France) to prepare a Ph.D. thesis in Automatic Control.

A. El Hajjaji

Ahmed El Hajjaji received his Ph.D. degree in automatic control from the University of Picardie Jules verne, France in 1993. He was an Associate Professor in the same university from 1994 to 2003. He is currently a Full Professor in the University of Picardie Jules Verne. Since 2001, he has also been the head of the research team of control and vehicle of Modeling, Information and Systems (MIS) laboratory. His current research intrests include fuzzy control, vehicle dynamics, fault-tolerant control, neural networks, manglev systems, and renewable energy systems.

R. Ceschi

Roger Ceschi received his Ph.D. degree in signal processing from the University of Paris-Sud Orsay, France in 1979. He was the General Director of the Graduate National School and Electronics Applications (E.N.S.E.A) from 1993 to 1998, and he was the General Director of the Graduate School ESIEE (Amiens) from 1998 to 2010. Between 2010 and 2011, he worked as an Advisor of the General Director of the Graduate School ESIEE (Paris). He worked as the General Director of the Graduate School ESME -Sudria from 2011 to 2013. Since 2014, he has been the General Director of the Graduate School Esigetel and the Deputy Director of the EFREI Group.