This paper focuses on the asynchronous finite-time control of discrete-time impulsive switched positive time-delay systems (SPLTSs). The admissible edge-dependent average dwell time (AED-ADT) approach, in which the switching behavior is represented by a directed graph, is adopted in this paper to reduce the conservatism of the mode-dependent average dwell time (MDADT) method. The new sufficient conditions for the existence of a family of asynchronously switched controllers are derived by constructing the co-positive Lyapunov functional (CLF) for asynchronous intervals and the multiple piecewise co-positive Lyapunov functional (MPCLF) for synchronous intervals, ensuring that the resulting closed-loop system is finite-time stable. Then, the desired controller gains can be obtained by solving a standard linear programming (LP) problem. Finally, two numerical examples are presented to demonstrate the validity of the developed results.
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