Inspired by the results obtained in Liu et al . (2008, 2009), this study extends the constrained control problem to singular linear positive discrete‐time systems with delay. By using the singular value decomposition approach, delay‐dependent sufficient conditions for the regularity, causality, positivity and exponential stabilisation with a given decay rate of the system are established in terms of linear programming problem. A numerical example to demonstrate the effectiveness of the proposed method is given.