Robust estimation design for unknown inputs fuzzy bilinear models: Application to faults diagnosis

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. Sufficient 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.