  We provide a method to construct finite abstractions exactly bisimilar to
linear systems under a modified periodic event-triggered control (PETC), when
considering as output the inter-event times they generate. Assuming that the
initial state lies on a known compact set, these finite-state models can
exactly predict all sequences of sampling times until a specified Lyapunov
sublevel set is reached. Based on these results, we provide a way to build
tight models simulating the traffic of conventional PETC. These models allow
computing tight bounds of the PETC average frequency and global exponential
stability (GES) decay rate. Our results are demonstrated through a numerical
case study.
