  Unnecessary communication and computation in the periodic execution of
control tasks lead to over-provisioning in hardware design (or
underexploitation in hardware utilization) in control applications, such as
networked control systems. To address these issues, researchers have proposed a
new class of strategies, named event-driven strategies. Despite of their
beneficiary effects, matters like task scheduling and appropriate dimensioning
of communication components have become more complicated with respect to
traditional periodic strategies. In this paper, we present a formal approach to
derive an abstracted system that captures the sampling behavior of a family of
event-triggered strategies for the case of LTI systems. This structure
approximately simulates the sampling behavior of the aperiodic control system.
Furthermore, the resulting quotient system is equivalent to a timed automaton.
In the construction of the abstraction, the state space is confined to a finite
number of convex regions, each of which represents a mode in the quotient
system. An LMI-based technique is deployed to derive a sampling time interval
associated to each region. Finally, reachability analysis is leveraged to find
the transitions of the quotient system.
