Definition of Reset Control System and Basic Results
In this chapter, the main goal is to arrive at a formal definition of a reset control system, or a reset system in general. This means that a definition of a reset control system solution will be given and analyzed. In general, as it is common to impulsive systems, reset systems may exhibit different types of solutions, in particular having complex patterns such as beating, deadlock, and Zenoness. In control practice, this type of behavior is considered pathological, and thus several conditions will be given for reset control systems to be well-posed. On the other hand, important properties of reset systems may be derived by analyzing the reset instants that correspond to a given initial condition. These patterns will be also analyzed, and their relationship with the observability and reachability of the base linear system will be shown. This chapter is based on (Baños and Mulero in On the well-posedness of reset control systems. Technical Report. University of Murcia, 2010).
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