Stability analysis of fractional order systems based on T-S fuzzy model with the fractional order

This paper addresses the problems of the robust stability and stabilization for fractional order systems based on uncertain Takagi-Sugeno fuzzy model. A sufficient condition of asymptotical stability for fractional order uncertain T-S fuzzy model is given, and a parallel distributed compensating fuzzy controller is designed to asymptotically stabilize the model. The sufficient conditions are formulated in the format of linear matrix inequalities. The fractional order T-S fuzzy model of a chaotic system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the approach is tested on fractional order Rossler system and fractional order uncertain Lorenz system.