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.