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This paper suggests a new stability analysis theorem dedicated to a class of fuzzy logic control systems. The fuzzy logic control systems consist of nonlinear Single Input-Single Output (SISO) discrete-time processes controlled by Takagi-Sugeno fuzzy logic controllers. The stability analysis is conducted on the basis of Lyapunov's direct method with quadratic Lyapunov function candidates. The theorem proves that if the derivative of the Lyapunov function candidate is negative definite in the active region of each fuzzy rule then the fuzzy logic control system will be asymptotically stable in the sense of Lyapunov. Sufficient stability conditions are offered. An example related to the design of a stable fuzzy logic control system for the discrete-time Lorenz chaotic system and simulation results are included.