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Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying
Xia Zhou1, Xing Zhou2, Jun Cheng3
1School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China; Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guilin 541002, China.
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.
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