LMI-based non-quadratic stabilization conditions for T-S fuzzy systems with delays in state and input

This paper investigated the stabilization and stability problems for the Takagi-Sugeno (T-S) fuzzy systems with delays in state and input. Based on the non-parallel distributed compensation (non-PDC) technology, a fuzzy controller with non-PDC control laws is proposed to stabilize the T-S fuzzy systems with delays in state and input. For relaxing the stabilization conditions, a parameter-dependent Lyapunov function (PDLF) is employed for the time-delay T-S fuzzy systems. By adopting a PDLF and applying the proposed fuzzy non-PDC controller, the delay-dependent non-quadratic stabilization conditions for the T-S fuzzy systems with delays in state and input are presented in terms of linear matrix inequalities (LMIs) to guarantee the asymptotic stabilization of the fuzzy system. Finally, two numerical examples are provided to demonstrate that the proposed stability conditions are less conservative than some quadratic approaches and the proposed non-PDC fuzzy controller is effective.