Event-triggered and self-triggered control have been proposed in recent years as promising control strategies to reduce communication resources in networked control systems (NCSs). Based on the notion of set-invariance theory, this note presents new self-triggered control strategies for linear discrete-time systems subject to input and state constraints. The proposed schemes not only achieve communication reduction for NCSs, but also ensure both asymptotic stability of the origin and constraint satisfactions. A numerical simulation example validates the effectiveness of the proposed approaches.