This paper introduces an observer-based neural quadratic sliding mode control strategy for interconnected Markov jump systems faced with unknown interconnections, regardless of the high dimensionality of the systems. Firstly, a dynamic event-triggered scheme is constructed in the communication channel to the Lebesgue state observer, with which an integral quadratic sliding mode hyperplane is put forward; Secondly, a neural-based control method is put forward to make sure that predefined sliding hyperplane is attractive; In addition, the occurrence of Zeno phenomenon is also verified to be avoided with the implementation of the controller; Thirdly, linear matrix inequality technique and Lyapunov stochastic stability theory are proposed to check the stochastic stability of closed-loop systems, including sliding mode dynamics and error dynamics; Finally, simulation results on single-link robot arms are given to reveal the validity of the obtained results.

The paper proposes an adaptive controller design for Markov jump systems with mixed mode transition information through a reduced-order sliding mode approach. The stability criteria and mode-dependent adaptive control law are achieved using linear matrix inequality technique. Firstly, a linear reduced-order sliding surface function is proposed to achieve the reduced-order sliding mode dynamics. Secondly, a feasible approach is presented to check the stochastic stability of resulting sliding motion corresponding to different mode transition information, and to solve the controller gains from stability criteria. Thirdly, an adaptive sliding mode controller is also designed to ensure the finite-time reachability of the predefined hyperplane even when no mode information is available. Finally, the application of the proposed control strategy to the RLC circuit is provided.