  This paper proposes a robust self-triggered distributed model predictive
control (DMPC) scheme for a family of Discrete-Time linear systems with local
(uncoupled) and global (coupled) constraints. To handle the additive
disturbance, tube-based method is proposed for the satisfaction of local state
and control constraints. Meanwhile, A special form of constraints tightening is
given to guarantee the global coupled constraints. The self-triggering
mechanism help reduce the computation burden by skip insignificant iteration
steps, which determine a certain sampling instants to solve the DMPC
optimization problem in parallel ways. The DMPC optimization problem is
constructed as a dual form, and solved distributedly based on the Alternative
Direction Multiplier Method (ADMM) with some known simplifications. Recursive
feasibility and input-to-state stability of the closed-loop system are shown,
the performance of proposed scheme is demonstrated by a simulation example.
