Disturbance Observer-Based H ∞ Control for Interval Type-2 Fuzzy Hidden Markov Jump Systems Subject to Deception Attacks

This article presents a composite anti-disturbance security control approach for the continuous-time nonlinear hidden Markov jump systems, in which the nonlinearities are characterized by the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model. To offset and suppress the influence of multiple disturbances on the system stability, a composite control method based on disturbance observer and ${\mathcal {H}}_{\infty }$ control is established. In addition, considering potential cyber-attacks, this article takes deception attacks as an example, assuming that the attack signal is generated by a nonlinear bounded function, and the Bernoulli distribution is employed to depict whether the attack occurs or not. Then, in accordance with the IT2 T-S fuzzy model, the final composite system is derived. With the help of tools, such as the Lyapunov stability theory and fuzzy theory, the stability of the target system is analysed, and the specific forms of the fuzzy composite controller and disturbance observer are obtained. Finally, the correctness and effectiveness of the control method proposed in this article are verified through two examples.