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

Abstract

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 pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ 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.