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1 Introduction
In the recent past decades, the design of unknown input observer (UIO) plays an
essential role in robust model-based fault detection. Fruitful results on the case of
unknown input linear system can be found in survey papers (Darouach et al.
1994
;
Guan and Saif
1991
; Hou and Muller
1992
; Yang and Wilde
1988
) and many types
of full order and reduced order unknown input observers are now available.
However, many physical systems are nonlinear in nature. For such system, the
use of the well known linear techniques may reduce in bad performance and even
instability. Generally, analysis for nonlinear systems is a quite involved procedure.
These last decades, a T-S fuzzy approach to represent or approximate a large class
of nonlinear systems is developed. It is well known that T-S fuzzy model is an
effective tool in the analysis and synthesis for nonlinear control systems (Azar
2010a
; Chadli and Borne
2012
,
2013
; Takagi and Sugeno
1985
; Taniguchi et al.
2000
). Indeed, the nonlinear model is approximated by a set of linear local models
connected by if-then rules and the resulting T-S fuzzy model can universally
approximate or exactly describe general nonlinear systems (Takagi and Sugeno
1985
; Tanaka et al.
1998
; Tanaka and Sugeno
1992
; Tanaka and Wang
2000
). In
the last two decade, numerous results have been devoted to observers design of
fuzzy T-S systems (Azar
2010b
,
2012
; Bergsten et al.
2002
; Chadli
2010
; Chadli
and Guerra
2012
;Ma
2002
; Ma and Sun
2001
; Tong and Tang
2000
; Yoneyama
et al.
2000
). These results use different techniques such as linear matrix-inequality
approach, sliding mode techniques, adaptive methods, etc. Moreover, it is noted
that all of the aforementioned fuzzy systems are based on the T-S fuzzy model with
linear rule consequence.
As a special extension, fuzzy bilinear system based on the T-S fuzzy model with
bilinear rule consequence has attracted the interest of researchers (Li and Tsai
2007
;
Li et al.
2008
; Saoudi et al.
2010
,
2012a, c
,
2013b
; Tsai and Li
2007
). For example
robust stabilization for the T-S fuzzy bilinear models has studied in (Li and Tsai
2007
) and extension to the T-S fuzzy bilinear models with time-delay is given in Tsai
and Li (
2007
). The problem of robust stabilization for discrete-time fuzzy bilinear
models was considered in (Li et al.
2008
). The synthesis of fault diagnosis and fault
tolerant control, have been proposed for this class of systems in Saoudi et al. (
2013a
,
2012c
). Moreover, several works are devoted to the state estimation by the use of
T-S models with measurable decision variables which are especially represented by
the input variables or the outputs of the system (Chadli and Coppier
2013
; Chadli
and Karimi
2012
; Gao et al.
2008
; Lendek et al.
2010
; Liu and Zhang
2003
). For
example, (Tanaka et al.
1998
) proposed a study of stability and stabilization by
multiple controllers. Patton et al. (
1998
) proposed an observer based on the
Luenberger observer structure, which was then used for the diagnosis. Ichalal et al.
(
2009
) developed an observer-based approach for robust residual generator and
diagnosis in nonlinear systems described by T-S fuzzy models. Gao et al. (
2008
)
presented a fuzzy state observer design for T-S fuzzy systems with application to
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