Abstract
This paper mainly investigates the event-triggered asynchronous control problem for two-dimensional (2-D) Markov jump systems (MJSs) with varying state delays. The asynchronous phenomenon that characterized by the mismatched modes between system and controller is treated with a hidden Markov model (HMM). An event-triggering strategy is adopted in controller design to reduce the burden of the communication network. Linear matrix inequality (LMI) based sufficient conditions are developed such that the closed-loop system is asymptotically stable and satisfies a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> noise attenuation performance index. Moreover, the event-triggered asynchronous control problem for systems without delays and the regular asynchronous control problem for systems with delays are studied as well, which can be treated as special cases of the main problem. Finally, an asynchronous controller design algorithm is proposed, whose effectiveness is demonstrated by two numerical examples.
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