  Impulsive dynamical systems is a well-established area of dynamical systems
theory, and it is used in this work to analyze several basic properties of
reset control systems: existence and uniqueness of solutions, and continuous
dependence on the initial condition (well-posedness). The work scope is about
reset control systems with a linear and time-invariant base system, and a
zero-crossing resetting law. A necessary and sufficient condition for existence
and uniqueness of solutions, based on the well-posedness of reset instants, is
developed. As a result, it is shown that reset control systems (with strictly
proper plants) do no have Zeno solutions. It is also shown that full reset and
partial reset (with a special structure) always produce well-posed reset
instants. Moreover, a definition of continuous dependence on the initial
condition is developed, and also a sufficient condition for reset control
systems to satisfy that property. Finally, this property is used to analyze
sensitivity of reset control systems to sensor noise. This work also includes a
number of illustrative examples motivating the key concepts and main results.
