Non-linear fuzzy control : LMI vs. sum of squares

Abstract

Recently, new system analysis techniques are available to study nonlinear dynamical systems using the sum of squares decomposition. Developing such techniques, using Takagi-Sugeno and Layponuv stability, is done throughout this project with the aid of the SOSTOOLS in MATLAB. The dynamical system can be represented by Takagi-Sugeno fuzzy model, thus this model can be simulated and studied using SOSTOOLS. Moreover, an analysis of the obtained model is done using the Linear Matrix Inequality (LMI) tools; then, a comparison was undertaken between the LMI and SOS. The main advantage of the SOSTOOLS is that it can solve equality and inequality constraints; thus, the stability conditions are more general and relaxed. Finally, to elucidate the validity and applicability of the proposed approach, an example is studied and conclusions are made.