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Robust Estimation Design for Unknown
Inputs Fuzzy Bilinear Models: Application
to Faults Diagnosis
Dhikra Saoudi, Mohammed Chadli and Naceur Benhadj Braeik
Abstract This present chapter addresses the robust estimation problem for a class
of nonlinear systems with unknown inputs and bilinear terms. The considered
nonlinear system is represented by Takagi-Sugeno (T-S) Fuzzy Bilinear Model
(FBM). Two cases are considered: the
first one deals with the study of FBM with
measurable decision variables and the second one assumes that these decision
variables are unmeasurable. Then, the proposed Fuzzy Bilinear Observer (FBO)
design for fuzzy bilinear models subject to unknown inputs is developed to ensure
the asymptotic convergence of the error dynamic using the Lyapunov method.
Stability analysis and gain matrices determination are performed by resolving a set
of Linear Matrices Inequalities (LMIs) for both cases. The design conditions lead to
the resolution of linear constraints easy to solve with existing numerical tools. The
given observer is then applied for fault detection. This chapter studies also the
problem of robust fault diagnosis based on a fuzzy bilinear observer. Suf
cient
conditions are established in order to guarantee the convergence of the state
estimation error. Thus a residual generator is determined on the basis of LMI
conditions such that the estimation error is sensitive to fault vector and insensitive
to the unknown inputs. These results are provided for measurable and unmeasurable
decision variables cases. The performances of the proposed estimation and fault
diagnosis method is successfully applied to academic examples.
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