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Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate bisimilarity is introduced. This paper aims to establish a modal characterization for alternating approximate bisimilarity. Based on this result, we provide a link between specifications satisfied by the samples of control systems with disturbances and their finite abstractions. Moreover, a simple example is given to illustrate the application of such link in the design of controller of control systems.

A modal characterization of alternating approximate bisimilarity