Security Control of Interval Type-2 Fuzzy Singularly Perturbed Hidden Markov Jump Systems: Dissipativity-Based Static Output Feedback

The dissipative control problem is investigated in this article for nonlinear hidden Markov jump systems with singular perturbation parameter (SPP) under replay attacks. Thereinto, an interval type-2 T-S fuzzy model is used to characterize the nonlinearities together with uncertainties. Meanwhile, a detection method combined with multisensor scheme is introduced to compensate for the damage to system stability by replay attacks. Based on the detection scheme, a fuzzy-mode-dependent controller based on static output feedback control is also constructed to enable the original systems to maintain robust operation even attacked. Then, by resorting to an improved Lyapunov function that depends on both the singular perturbation parameter and jump modes, some sufficient conditions, ensuring the stochastic stability and strict $(Q,S,R)$ -dissipativity of the resulting systems, are deduced in theory. Furthermore, the gains of the constructed controller are calculated by solving the matrix convex optimization problem. Finally, the efficacy and practicality of the obtained results are verified via two examples.