• Event-based
• event-triggered
• PID controllers

In recent years, control system theory an essential part of the
development of many devices, from complex critical systems, as
airplanes and cars, to less critical systems like home appliances.
Many of this systems interact with the environment which presents
continuos-varying input signals. The most common way to design a
control algorithm is to periodically sample and digitize the input
signals before processing them. In complex systems, each control
algorithm is implemented as a software task that is executed by a
real-time operating system that has to coordinate several other
activities, like input/output operations, human-machine interfaces,
or other control algorithms for different control loops. The
real-time operating system usually runs on a hardware platform with
limited resources, in terms of computational power, memory, and
sometimes also energy. For example, many embedded devices are
powered by batteries, and one possible objective is to reach some
control goal with minimum energy.

A software implementation based on periodic sampling may not be the
best solution for systems, since it performs the sampling and the
control algorithm computation anyway, independently of the state of
the system. The main reason for using periodic time-driven system is
that they are based on a consolidated theory, so they are easier to
analyse and implement.

In order to increase the efficiency of the implementation, several
researcher are proposing to use \emph{event-driven paradigms}. In
event-driven systems, the control algorithm is only performed when
an event is triggered by certain conditions on the input signal. In
this way, the computational and communication resources are only
used when it is necessary to use them, hopefully saving on resource
usage.

However, the theory behind event-driven control algorithms is still
not well understood, because it is grounded in the theory of
nonlinear systems and linear time varying systems. However the
scientific community is working hard to find how to model such
systems and to give useful tools to analyse and study systems based
on the event-driven paradigm.

In this thesis, different approaches to event-driven control systems
are analysed. We describe the problems they present and how they can
be modeled. A general paradigm for the design of an event-driven
control platform has been implemented, using appropriate variants of
the classical PID control algorithm. Further, a step forward has
been done in modeling and analysing a new nonlinearity that arises
when using a particular sampling criterion.