Asynchronous Control of Networked Markov Jump Linear Systems Under DoS Attacks

This article intends to study the asynchronous $\mathscr {H}_{\infty } $ control problem for discrete-time networked Markov jump linear systems (MJLSs) subject to aperiodic denial-of-service (DoS) attacks. A more practical scenario of the simultaneous presence of imperfect mode detection and imperfectly known probability information is considered. More specifically, we use a hidden Markov model (HMM) to characterize the mismatched detected/system modes, and a general description of imperfectly known probabilities to characterize both the transition and observation probabilities (T/OPs). Then, we propose an HMM-based asynchronous control law for the concerned networked MJLS, and several sufficient conditions are established to ensure its stochastic stability and $\mathscr {H}_{\infty } $ performance, by means of an iterative method of piecewise Lyapunov functional and a nonconservative probability decoupling principle. We also show that the asynchronous control law can be designed via an LMI-based convex optimization algorithm. In the end, we use an example of a single-link robotic arm to demonstrate the effectiveness of the obtained results.