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This paper studies the fault tolerant control (FTC) problem for a class of nonlinear discrete-time systems with guaranteed Hinfin performance objective in the presence of actuator faults. The mode of faults under consideration is typical aberration of actuator effectiveness. The novelty of this paper is that the effect of the nonlinear terms is described as an index in order to transform the FTC design problem into a semi-definite programming (SDP). The proposed optimization approach is to find zero optimum for this index. Combined with Hinfin performance index, the conceived multi-objective optimization problem is solved by using sum of squares method (SOS) in a reliable and efficient way. A numerical example is included to verify the applicability of this new approach for the nonlinear FTC synthesis.