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This paper presents a stability analysis approach for a class of nonlinear processes controlled by Mamdani type fuzzy logic controllers (FLCs). The stability analysis is performed in the sense of Lyapunov dedicated resulting in the derivation of an original stability analysis approach that can be used as design method for FLCs with guaranteed stability. Quadratic positive definite Lyapunov functions candidate are employed in this context. The approach is expressed in terms of sufficient stability conditions for fuzzy logic control systems with Mamdani type FLCs. An illustrative example validates the stability analysis approach by designing an FLC to control a nonlinear process