Nonstationary quantized control for discrete-time Markov jump singularly perturbed systems against deception attacks *

This paper addresses the nonstationary quantized control problem for the discrete-time Markov jump singularly perturbed systems (MJSPSs) subject to deception attacks (DAs). The control inputs are characterized by randomly occurring DAs and nonstationary quantization simultaneously, where the DAs are depicted by means of a Bernoulli distributed sequence. By applying a multi-layer structure methodology (MLSM), the nonstationary controllers are devised for MJSPSs. Meanwhile, the correlation among system mode, controller mode, and quantizer mode are portrayed via the nonstationary Markov process. Based on a mode-dependent Lyapunov functional, sufficient criteria are established such that the resulting closed-loop system (CLS) is stochastic mean square exponential ultimately bounded (SMSEUB), and the desired controller is designed. Ultimately, two simulation examples are offered to elaborate on the validity and superiority of the proposed theoretical results. (c) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper addresses the nonstationary quantized control problem for the discrete-time Markov jump singularly perturbed systems subject to deception attacks. A multi-layer structure methodology is applied to devise nonstationary controllers, and criteria are established based on mode-dependent Lyapunov functional to ensure the resulting closed-loop system is stochastic mean square exponential ultimately bounded. Two simulation examples are provided to demonstrate the validity and superiority of the proposed theoretical results.