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This paper investigates a geometric property of timeoptimal problem in the Takagi-Sugeno (T-S) fuzzy model via Lie algebra. We will focus on the existence of a time-optimal solution, singularity of switching function, and number of switching. These inherent problems are considered because of their rich geometric properties. The sufficient condition for the existence of a timeoptimal solution reveals the controllability of T-S fuzzy model that can be found by the generalized rank condition. Thedoi:10.1109/tfuzz.2008.924321 fatcat:j2e6jfj7fvd7rpp6mg3dhxy6ie