Adaptive neural-network-based sliding mode control of switching distributed delay systems with Markov jump parameters

This paper is devoted to the issue of observer-based adaptive sliding mode control of distributed delay systems with deterministic switching rules and stochastic jumping process, simultaneously, through a neural network approach. Firstly, relying on the designed Lebesgue observer, a sliding mode hyperplane in the integral form is put forward, on which a desired sliding mode dynamic system is derived. Secondly, in consideration of complexity of real transition rates information, a novel adaptive dynamic controller that fits to universal mode information is designed to ensure the existence of sliding motion in finite-time, especially for the case that the mode information is totally unknown. In addition, an observer-based neural compensator is developed to attenuate the effectiveness of unknown system nonlinearity. Thirdly, an average dwell-time approach is utilized to check the mean-square exponential stability of the obtained sliding mode dynamics, particularly, the proposed criteria conditions are successfully unified with the designed controller in the type of mode information. Finally, a practical example is provided to verify the validity of the proposed method.