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When designing interval observers for switched systems, for simplicity, it is always assumed that the switching signal of interval observers is synchronised with one of subsystems. However, in fact, they are asynchronous in most cases. In this study, the interval observer design problem for discrete-time switched systems with asynchronous switching law is investigated. At first, a robust observer is designed based on the H ∞ observer theory. Then, in order to reduce the conservatism of designdoi:10.1049/iet-cta.2019.0750 fatcat:3lpw5rgt7fdv7djjil6te3blve