Observer-Based Adaptive SMC for Nonlinear Uncertain Singular Semi-Markov Jump Systems With Applications to DC Motor

This paper deals with the observer-based adaptive sliding mode control (OBASMC) design for nonlinear uncertain singular semi-Markov jump systems. The system satisfies the singular property and follows a stochastic semi-Markov process related to Weibull distribution. Due to the influence of sensor factors in practical systems, the state vectors are not always known. Additionally, the unavoidable measurement errors in the actual system always lead to the model uncertainties and the unknown nonlinearity. Our attention is to design the OBASMC law for such a class of complex systems. First, by the use of the Lyapunov–Krasovskii functional, sufficient conditions are given, such that the sliding mode dynamics are stochastically admissible. Then, the OBASMC law is proposed to guarantee the reachability in a finite-time region. Finally, the practical system about dc motor model is given to verify the validity.