Nonlinear Fault-Tolerant Control Design for Singular Stochastic Systems With Fractional Stochastic Noise and Time-Delay

This work focuses on the stabilization issue for a class of singular stochastic systems against fractional Gaussian noise driven by fractional Brownian motion. In particular, the system is formulated with time-delay, nonlinear actuator faults and randomly occurring parameter uncertainties. Primarily, a fractional-infinitesimal operator is incorporated to deal with the fractional Ito stochastic systems in the derivation part of Lyapunov-based stability analysis. Further, the considered system is subjected to both linear and nonlinear actuator faults and the stabilization will be achieved by the consideration of a nonlinear resilient fault-tolerant proportional-retarded controller. By incorporating the fractional-infinitesimal operator and with the choice of a relevant Lyapunov-Krasovskii functional candidate, a new adequate criterion is deduced by means of linear matrix inequalities. Then the established inequalities are then solved for obtaining the controller gain matrices. Thereafter, an example illustrating the effectiveness and applicability of the proposed results is provided.