Real-time state range estimation of asynchronous Markov jump linear systems with bounded disturbance and random cyber attack

This paper deals with the real-time state range monitoring problem of a class of Markov jump linear system (MJLS) subject to random injection attacks and bounded disturbance by an asynchronous interval observer method. Considering the noised effect of random attacks on output measurement, a Luenberger-like interval observer with asynchronous jumping parameters is constructed by using the dynamic boundary information of attack and disturbance flexibly, where a hidden Markov model is actively introduced to model the asynchronous jumping behavior. Using the observer, the positivity of interval estimation error systems is ensured. To overcome the optimization design difficulty of the interval observer, a unified positive hidden MJLS is developed, where the observer gain matrices and the disturbance input are separated explicitly. Some attack-frequency-dependent conditions for stochastic l1-gain performance analysis and observer design optimization are provided by linear programming. For the method validation purpose, a secure remote monitoring task of DC motor in both unstable and stable situations is provided in case study.