Mean-square admissibility for stochastic T-S fuzzy singular systems based on extended quadratic Lyapunov function approach

The mean-square admissibility problem of stochastic T-S fuzzy singular systems via an extended quadratic Lyapunov function is investigated in this paper. Comparing with the existing quadratic Lyapunov function method, the extended quadratic Lyapunov function method can relax stabilization conditions. Firstly, the sufficient condition is given for the mean-square admissibility of stochastic T-S fuzzy singular systems based on an extended quadratic Lyapunov function approach. Secondly, two sufficient conditions for mean-square admissibility of closed-loop systems via the parallel distributed compensation (PDC) fuzzy controller and non-parallel distributed compensation (non-PDC) fuzzy controller are proposed. Furthermore, through the extended quadratic Lyapunov function method and non-PDC fuzzy controller, the less conservative mean-square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities (LMIs). Finally, some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology.