Stabilization conditions for fuzzy control of uncertain fractional order non‐linear systems with random disturbances

Abstract

A novel fractional order Takagi–Sugeno (T–S) fuzzy control method for a class of fractional order non‐linear systems is proposed in this study. On the basis of the fractional order interval theory, the generalised T–S fuzzy model for a class of uncertain fractional order non‐linear systems is presented. By using fractional order Lyapunov stability theorem, the more relaxed and practical sufficient stability conditions which are presented as a new set of linear matrix inequalities are put forward, which are guaranteed by rigorous mathematical derivation. The proposed control scheme is developed for fractional order non‐linear systems stabilisation in the presence of random disturbances. Typical instances including the fractional order three‐dimensional (3D) non‐linear system and the fractional order 4D non‐linear Lorenz hyperchaos are implemented. Simulation results indicate the designed fractional order T–S fuzzy control scheme works well compared with the existing method.