Robust Delay-dependent Stability of Nonlinear Stochastic Systems Subject to Passivity Performance

Abstract

The delay-dependent stability issue of nonlinear stochastic systems with external disturbance is investigated in this paper subject to passivity performance. Based on the Takagi-Sugeno (T-S) fuzzy model, the It & ocirc; formula and Lyapunov function are directly applied to discuss the stability issue. And, some perturbations are considered to represent the uncertainty for discussing the robustness. Moreover, the interval time-varying case represents the time delay effect on the system. A novel Lyapunov function is proposed to develop the stability criterion with the composing fuzzy positive definite matrix for reducing conservatism. Furthermore, a free-matrix-based inequality is employed to introduce some variables for increasing the freedom of calculation. Based on the proposed criterion, the less conservative delay-dependent stability criterion is applied to design a fuzzy controller such that the nonlinear stochastic system is robust asymptotically stable and passive in the mean square. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed design method.