Input-to-State Stabilization for Markov Jump Systems with Dynamic Quantization and Multimode Injection Attacks

Jianping Zhou, Jingjing Dong, Shengyuan Xu, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review


This article explores observer-based input-to-state stabilization for Markov jump systems with both dynamic input and output quantization, as well as multimode injection attacks (IAs). The Markov chain of the plant, together with the IAs described by two stochastic processes following the categorical distribution, constitutes a pair of hidden Markov models. A sufficient condition for mean-square input-to-state stability of the feedback control system is proposed utilizing a Lyapunov-type function dependent on both the mode and exponential decay rate, the S-procedure, as well as several stochastic analysis tools. Then, a two-stage approach, with which the required controller and observer gains and dynamic scaling factors can be determined successively, is developed. The scaling factors are constructed as piecewise functions, excluding the possibility of singularities involved in previous dynamic quantized control approaches. Under the zero initial condition, a greedy backtracking suboptimization algorithm is further put forward, offering an estimate of the minimum permissible upper bound of the mean-square closed-loop state for a bounded disturbance input, given a fixed exponential decay rate. Finally, a vertical lift aircraft model is applied to validate the proposed quantized observer-based control approach and suboptimization algorithm.

Original languageEnglish
Pages (from-to)2517-2529
Number of pages13
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number4
Publication statusPublished - 2024 Apr 1

Bibliographical note

Publisher Copyright:
© 2013 IEEE.


  • Dynamic quantization
  • Markov jump system (MJS)
  • injection attack (IA)
  • input-to-state stability
  • observer-based control

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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