Yonggui Kao received the B.E. degree from Beijing Jiaotong University in 1996. He received M.E. and Ph.D. degrees from Ocean University of China in 2005 and 2008, respectively. He now is a Professor at Department of Mathematics, Harbin Institute of Technology(Weihai). His research interest covers stochastic systems, impulsive systems, neural networks, stability theory and sliding mode control.Panpan Zhang received the B.Sc. degree in Mathematics and Applied Mathematics from Qufu Normal University, Qufu, China, in 2016. She received M.Sc. degree from Harbin University of Science and Technology,Harbin, China, in 2019. She is currently working toward the Ph.D. degree in Mathematics from Harbin Institute of Technology (Weihai). Her current research interests include time-delay systems, sliding mode control for networked systems, stochastic systems.

• Introduction.-  Sliding mode H ∞ control for Markov jump discrete systems under packet losses.- Finite-time boundedness.- Passivity and control synthesis.- Hidden Markov model-based control.- Sliding mode fault-tolerant control.- Bumpless transfer control.- semi-Markov jump systems.- Adaptive fault-tolerant control.- Conclusion and future research direction.

Yonggui Kao received the B.E. degree from Beijing Jiaotong University in 1996. He received M.E. and Ph.D. degrees from Ocean University of China in 2005 and 2008, respectively. He now is a Professor at Department of Mathematics, Harbin Institute of Technology(Weihai). His research interest covers stochastic systems, impulsive systems, neural networks, stability theory and sliding mode control.Panpan Zhang received the B.Sc. degree in Mathematics and Applied Mathematics from Qufu Normal University, Qufu, China, in 2016. She received M.Sc. degree from Harbin University of Science and Technology,Harbin, China, in 2019. She is currently working toward the Ph.D. degree in Mathematics from Harbin Institute of Technology (Weihai). Her current research interests include time-delay systems, sliding mode control for networked systems, stochastic systems.

• Introduction.-  Sliding mode H ∞ control for Markov jump discrete systems under packet losses.- Finite-time boundedness.- Passivity and control synthesis.- Hidden Markov model-based control.- Sliding mode fault-tolerant control.- Bumpless transfer control.- semi-Markov jump systems.- Adaptive fault-tolerant control.- Conclusion and future research direction.

Yonggui Kao received the B.E. degree from Beijing Jiaotong University in 1996. He received M.E. and Ph.D. degrees from Ocean University of China in 2005 and 2008, respectively. He now is a Professor at Department of Mathematics, Harbin Institute of Technology(Weihai). His research interest covers stochastic systems, impulsive systems, neural networks, stability theory and sliding mode control.Panpan Zhang received the B.Sc. degree in Mathematics and Applied Mathematics from Qufu Normal University, Qufu, China, in 2016. She received M.Sc. degree from Harbin University of Science and Technology,Harbin, China, in 2019. She is currently working toward the Ph.D. degree in Mathematics from Harbin Institute of Technology (Weihai). Her current research interests include time-delay systems, sliding mode control for networked systems, stochastic systems.

• Introduction.-  Sliding mode H ∞ control for Markov jump discrete systems under packet losses.- Finite-time boundedness.- Passivity and control synthesis.- Hidden Markov model-based control.- Sliding mode fault-tolerant control.- Bumpless transfer control.- semi-Markov jump systems.- Adaptive fault-tolerant control.- Conclusion and future research direction.