Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov–Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the $p$th moment exponential stability conditions are derived by utilizing the generalized fractional It$\hat{o}$ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.