  Event-triggered control and self-triggered control have been recently
proposed as new implementation paradigms that reduce resource usage for control
systems. In self-triggered control, the controller is augmented with the
computation of the next time instant at which the feedback control law is to be
recomputed. Since these execution instants are obtained as a function of the
plant state, we effectively close the loop only when it is required to maintain
the desired performance, thereby greatly reducing the resources required for
control. In this paper we present a new technique for the computation of the
execution instants by exploiting the concept of isochronous manifolds, also
introduced in this paper. While our previous results showed how homogeneity can
be used to compute the execution instants along some directions in the state
space, the concept of isochrony allows us to compute the executions instants
along every direction in the state space. Moreover, we also show in this paper
how to homogenize smooth control systems thus making our results applicable to
any smooth control system. The benefits of the proposed approach with respect
to existing techniques are analyzed in two examples.
