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This paper suggests a new stability analysis approach dedicated to a class of fuzzy control systems controlling multi input-multi output (MIMO) nonlinear processes by means of Takagi-Sugeno fuzzy logic controllers. The approach is based on LaSalle's global invariant set theorem, and an original stability theorem offers sufficient stability conditions. The applicability and efficiency of the theoretical results are illustrated by a MIMO case study dealing with the fuzzy control of a spherical three tank system.