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

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.