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This paper introduces the class of dual-random-rate systems (i.e., dual-rate systems with random output rates), which is well suited to model image-based control systems. It is shown that a dual-random-rate system can be reformulated as a switched linear system with a (quasi-periodic) random switching signal that is a static function of Markov chain. This reformulation makes it possible to study dual-random-rate systems with the stability and output performance analysis tools developed for Markov jump linear systems. The approach is illustrated via a practical example: the compensation of image drift in a transmission electron microscope.