Hidden Markov model‐based ℋ∞ control for singular Markov jump systems under denial of service attacks

This work investigates the ℋ∞$$ {\mathscr{H}}_{\infty } $$ control problem of discrete‐time singular Markov jump systems against denial of service attacks, in which the Markov state information is seen as restricted access. To solve this situation, a hidden Markov model is introduced. The main objective is to construct a controller with the help of hidden Markov model such that the stochastically admissible of the closed‐loop singular Markov jump systems with limited access mode information can be guaranteed under denial of service attacks. To produce the needed hidden Markov model‐based controller, a matrix contract transformation approach is developed. At the end, a numerical example and a tunnel diode circuit are presented to demonstrate the effectiveness and benefit of the design technique described in this research.