Improvement on stability conditions for continuous-time T-S fuzzy systems

This paper addresses the problem of stability analysis for continuous-time Takagi-Sugeno (T-S) fuzzy systems. A new series of line-integral Lyapunov functions (LILFs) is developed which can be seen as an extension of the existing LILF. Without the difficulty of dealing with the time derivatives of the membership functions, relaxed stability conditions are derived by combining the matrix Polya׳s theorem in terms of linear matrix inequalities. To further illustrate the effectiveness of the extended LILFs, the T-S fuzzy systems with time delay are also studied and corresponding relaxed stability conditions are obtained as well. Finally, several numerical examples are provided to illustrate the improvement of the proposed results.