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This article analyzes the problem of the sliding-mode control (SMC) design for discrete-time piecewise nonhomogeneous Markov jump nonlinear systems (MJNSs) subject to an external disturbance with time-varying transition probabilities (TPs). A discrete-time asynchronous integral sliding surface is constructed, which yields matched-nonlinearity-free sliding-mode dynamics (SMDs). Then, by using the mode-dependent Lyapunov function technique, a sufficient condition is established for ensuring the stochastic stability of SMD with extended dissipation. The solution to designing controller gains is obtained. Moreover, an SMC law and an adaptive law are, respectively, derived for driving the system trajectories to move into a predetermined sliding-mode region with specified precision. Finally, the feasibility and effectiveness of the new design are verified and demonstrated by a simulation example.
Dong et al. (Sat,) studied this question.