This brief introduces the concept of measure chain theory in order to design event-triggered controllers for systems evolving on arbitrary time domains. The event-triggering mechanism is derived from input-to-state (ISS) stable Lyapunov functions defined on measure chains. These results not only unify existing event-triggered controller design procedures for systems on continuous and discrete time domains, but also extend them to non-homogeneous time domains. Numerical simulations for systems on different measure chains illustrate the effectiveness of the designed event-triggered controllers.
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