This work focuses on the sliding mode control (SMC) of stochastic semi-Markovian switching linear parameter-varying (LPV) models in discrete case. In contrast to traditional LPV systems, semi-Markovian switching LPV models considered in this work are more in line with actual systems. The main contributions are that compared to traditional Lyapunov function, the considered Lyapunov function is related to the parameter variations with wide applications in the actual systems, and this work designs a suitable sliding mode controller that depends on the parameter variations to achieve the accessibility of sliding region, removing the related limitations. Based on the upper bound of the sojourn time for each mode and certain techniques for eliminating the nonlinear coupling terms with additional matrices, the underlying system realizes the stability criteria. Finally, a turbofan engine model is adopted to demonstrate the feasibility of the control method.
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