Stability analysis of fractional order systems based on T–S fuzzy model with the fractional order $$\alpha : 0<\alpha <1$$ α : 0 < α < 1

Abstract

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.