Fault detection, isolation and estimation for Takagi–Sugeno nonlinear systems

This article is dedicated to the problem of fault detection, isolation and estimation for nonlinear systems described by a Takagi–Sugeno (T–S) model. One of the interests of this type of models is the possibility to extend some tools and methods from the linear system case to the nonlinear one. The principle of the proposed strategy is to transform the problem of simultaneously minimizing the perturbation effect and maximizing the fault effect, on the residual vector, in a simple problem of L 2 - norm minimization. A linear system is used to define the ideal response of the residual signal to the fault. Then the aim is to synthesize a residual generator that both minimizes the difference between real and ideal responses and the influence of the disturbance. The minimization problem is formulated by the bounded real lemma (BRL) and linear matrix inequality (LMI) formalism. After studying the general framework, a special case of systems with actuator and sensor faults is considered where the fault incidence matrix is not full column rank. Simulation examples are given to illustrate the proposed method. Finally, Polyaʹs theorem is used to reduce the conservatism of the proposed result. The obtained relaxation is also illustrated by a numerical example.