Passivity and passification of T-S fuzzy descriptor systems with stochastic perturbation and time delay

Abstract

This study is concerned with the passivity and passification problems for Takagi–Sugeno fuzzy descriptor systems subject to stochastic perturbation and time-varying delay. The stochastic disturbance is given in the form of one-dimensional Brownian motion and the delay is assumed to be time-varying and differentiable. By utilising the Lyapunov functional method and the stochastic analysis techniques, a delay-dependent criterion is presented to ensure that the considered system is regular, impulse-free, asymptotically stable in the mean-square sense and passive in the sense of expectation. Then, based on this criterion, two procedures are proposed for designing state-feedback controller, which guarantee the resulting closed-loop system admissible and passive in the sense of expectation. All conditions are cast in terms of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the validity and applicability of the proposed results.