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 design

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... nditions and improve the performance of the interval observer, the zonotope method is applied to estimate the bounds of system state. Finally, two examples are provided to highlight the efficiency of the proposed method. Nomenclature x ≤ y components of x are less than the corresponding components of y ⊕ Minkowski sum ⊙ linear mapping A ≺ 0 A is a negative definite matrix ∥ x ∥ Euclidean norm of the vector x, i.e. x T x I identity matrix with appropriate dimensions ϕ(P) minimum value among all eigenvalues of matrix P ϕ(P) maximum value among all eigenvalues of matrix P