Disturbance Observer-Based Linear Matrix Inequality for the Synchronization of Takagi-Sugeno Fuzzy Chaotic Systems

This article presents a synchronization control method based on poles' placement, disturbances, and uncertainty estimation (DUE) for a pair of Takagi-Sugeno fuzzy systems. First, a 3-D chaotic system was completely converted into a Takagi-Sugeno (T-S) fuzzy model by applying the nonlinearity sector method, which consists of if-then rules and sub-linear systems. Second, two identical T-S fuzzy systems with different initial conditions were synchronized by applying the linear matrix inequality (LMI) to place the eigenvalues of the state error equations in the stable region. Third, the sum of the time-varying disturbances and uncertainties of two nonidentical T-S fuzzy systems were deleted by a disturbance and uncertainty estimation. The given output signals confirmed that the proposed method is suitable and ideal for synchronizing T-S fuzzy systems. The ideas of control theory were implemented by using two experimental scenarios in MATLAB Simulink for two computers connected via an internet router and an electronics circuit's communication.