This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to zero, thus avoiding the numerical stiffness due to the interaction of two different dynamics. The fault tolerant controller is computed in two steps. First, a nominal composite controller is designed using the reduced subsystems. Secondly, an additive part is combined with the basic controller to overcome the fault effect. The derived ε -independent controller guarantees asymptotic stability despite the presence of actuator faults. The Lyapunov stability theory is used to prove the stability provided the singular perturbation parameter is sufficiently small. The theoretical results are simulated using a numerical application.K e y w o r d s: nonlinear time-invariant singularly perturbed systems, singular perturbation method, additive fault tolerant control, actuator defect, Lyapunov theory

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The additive fault tolerant control (FTC) for delayed system is studied in this work. To design the additive control, two steps are necessary; the first one is the estimation of the sensor fault amplitude using a Luenberger observer with delay, and the second one consists to generate the additive fault tolerant control law and to add it to the nominal control of delayed system. The additive control law must be in function of fault term, then, in the absence of fault the expression of additive control equal to zero. The generation of nominal control law consist to determinate the state feedback gain by using the Lambert W method. Around all these control tools, we propose an extension of the additive FTC to delayed singularly perturbed systems (SPS). So, this extension consists to decompose the delayed SPS in two parts: delayed slow subsystem (delayed SS) and fast subsystem (FS) without time delay. Next, we consider that the delayed SPS is affected at its steady-state, and we apply the principal of FTC to the delayed SS and finally we combine them with the feedback gain control of FS by using the principal of composite control

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