Event-based sliding mode control for fuzzy singular systems with semi-Markovian switching parameters

This paper addresses the observer-based dynamic event-triggered (DET) sliding mode control (SMC) problem for fuzzy singular semi-Markovian jump systems (FSS-MJSs) subject to generalized dissipative performance, in which a novel double-quantized structure is reasonably merged into a unified model. The main aim of this paper is to develop a mode-dependent adaptive sliding mode control (ASMC) law through the DET rule, which not only makes the closed-loop systems mean-square admissibility and generalized dissipative, but also the finite-time reachability around the predefined sliding mode surface (SMS) can be achieved. Firstly, in order to improve the data transmission efficiency and save network bandwidth resources, DET and doubled-quantized-based control protocol are introduced, in which the event-based threshold function is dynamically regulated and the data of input and output are both quantized; Secondly, due to the sensor information constraints, system state information is not always obtained in practice, hence, a suitable observer design can make up for this defect. Meantime, in terms of elegant linearization technique and implicit function theorem, the uniqueness of the solution for FSS-MJSs is also established; Additionally, by making use of the Lyapunov functional and linear matrix inequality (LMI) technique, both the desired SMC gains, observer gains and triggering parameter matrices are co-designed, more than that the derivative singular matrix is also integrated into the whole design process such that the derived conditions are much more easily to be checked; Finally, a numerical example and a practical application example are co-given to verify the effectiveness of our design mentality. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper addresses the observer-based dynamic event-triggered sliding mode control problem for fuzzy singular semi-Markovian jump systems subject to generalized dissipative performance. It introduces a novel double-quantized structure and develops a mode-dependent adaptive sliding mode control law. Furthermore, it proposes a dynamically regulated event-based threshold function and quantized data transmission method. The uniqueness of the solution for the systems is established through suitable observer design and elegant linearization technique. The desired control gains, observer gains, and triggering parameter matrices are co-designed using Lyapunov functional and linear matrix inequality technique, with the integration of derivative singular matrix simplifying the verification process. Numerical and practical examples are provided to validate the effectiveness of the design.