Stability and l1-gain analysis for positive 2D T–S fuzzy state-delayed systems in the second FM model

This paper considers the problems of delay-dependent stability and l1-gain analysis for a class of positive two-dimensional (2D) Takagi–Sugeno (T–S) fuzzy linear systems with state delays described by the second FM model. Firstly, the co-positive type Lyapunov function method is applied to establish sufficient conditions of asymptotical stability for the addressed positive 2D T–S fuzzy system. Then, the l1-gain performance analysis for the positive 2D T–S fuzzy delayed system is studied. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the proposed method.