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Quantized Sliding Mode Control for Networked Markovian Jump Systems under Round-robin Protocol: The Output Feedback Case

Lijuan Nie, Dongyan Chen*, and Jun Hu*
International Journal of Control, Automation, and Systems, vol. 19, no. 8, pp.2674-2686, 2021

Abstract : This paper is concerned with the problem of protocol-based sliding mode control for a class of uncertain discrete networked Markovian jump systems with stochastic perturbation and time-varying delays. An improved dynamic uniform quantizer for processing system output signals is proposed to mitigate communication constraints. Next, a Round-Robin protocol with zero-order holders is introduced in the communication channels from the controller to the actuators to reduce potential network congestion and collision. Then, in the output feedback case, a new sliding surface is designed based on the quantized output, and a mode-dependent sliding mode controller is constructed using protocol scheduling signals. Additionally, a sufficient condition is derived to ensure that the closed-loop system is asymptotically stable in the mean square on a specific sliding surface despite the existence of the time-varying delays. Subsequently, the reachability of the state trajectories is guaranteed, where a sufficient criterion is proposed by constructing new Lyapunov-Krasovskii functional as well as using the stability theory. Furthermore, the cone complementary linearization iteration algorithm is employed to tackle the non-convex problem during the controller design. Finally, a simulation example demonstrate the effectiveness and feasibility of the protocol-based sliding mode control method.

Keyword : Cone complementary linearization, dynamic uniform quantizer, networked Markovian jump systems, sliding mode control, round-robin protocol.

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