Stabilisation for positive switched T-S fuzzy delayed systems under standard L1 and L∞ performance

In this paper, the stabilisation problem for positive switched T-S fuzzy delayed systems under standard L₁ and L_∞ performance is addressed. First, by proposing a time-scheduled multiple linear copositive Lyapunov function which is time-varying during the mode-dependent minimum dwell-time interval, sufficient conditions of asymptotical stability for positive switched T-S fuzzy delayed system under dwell-time switching are derived for the first time. Then, sufficient conditions for the underlying system to be asymptotically stable with standard L₁ and L_∞ performance are obtained, respectively. Based on the obtained results, a fuzzy state-feedback controller scheme is designed to stabilise the positive switched T-S fuzzy delayed system, while guaranteeing the positivity and asymptotical stability with standard L₁ performance in closed loop. Furthermore, the stabilisation problem under standard L_∞ performance is also solved. All the results are presented in the linear programming form. Finally, two numerical examples are presented to demonstrate the effectiveness of the obtained theoretical results.