Composite Anti-Disturbance Control for Nonlinear Hidden Markov Jump Systems Under Replay Attacks: A Dynamic Output-Feedback Method

This article is dedicated to researching the problem of composite anti-disturbance control for nonlinear hidden Markov jump systems, described by the interval type-2 Takagi-Sugeno fuzzy method, under replay attacks in the continuous-time domain. Based on dynamic output feedback control and disturbance observer, a fuzzy composite controller, following the core idea of nonparallel distribution compensation, is designed to compensate for the impact of multiple disturbances. For replay attacks, a multisensor scheme with the detection mechanism is introduced, enabling the studied systems to remain stable even under attacks. Afterward, with the aid of the Lyapunov stability theory, sufficient conditions for ensuring the stability of the resulting systems are deduced, and then the gains of the desired controller and disturbance observer are obtained. Finally, the rationality and effectiveness of the established method are demonstrated through simulation, as well as its superiority over the traditional ${\mathcal {H}}_{infty }$ control method.