Robust Fuzzy Control of Uncertain Nonlinear Systems Based on Linear Matrix Inequalities

Robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. Firstly, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires finding a common positive definite matrix in each maximal overlapped-rules group, can reduce the conservatism and difficulty of the former stability conditions. Finally, a simulation example shows the proposed approach is effective.