Mean square exponential stabilization of uncertain time-delay stochastic systems with fractional Brownian motion

This article is concerned with exponential mean square stabilization of stochastic systems driven by fractional Brownian motion subject to state-delay and uncertainties by sliding mode control. By applying the proposed method, the states of the system reach the sliding surface in finite time. Then, some sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the mean-square exponential stability of the sliding motion. The LMI conditions for mean-square exponential stability of the sliding mode dynamics are derived by constructing a novel Lyapunov functional. Finally, a simulation example is presented which corroborates the accuracy of the results.

Automated summary

This article addresses the exponential mean square stabilization of stochastic systems driven by fractional Brownian motion with state-delay and uncertainties through sliding mode control. The proposed method ensures that the states of the system reach the sliding surface in finite time. The use of linear matrix inequalities (LMIs) guarantees the mean-square exponential stability of the sliding motion, with conditions derived through a novel Lyapunov functional. A simulation example is provided to validate the results.