The averaging method for control design and stability analysis of practical switched systems

Switched models provide a suitable framework for many practical control systems. At a certain level of abstraction smooth models obtained by averaging switched models are able to capture most relevant properties of the system behavior. Stability and control design for a nonsmooth switched system can be inferred by analyzing the smooth averaged system. In this paper these advantages emerging from the use of averaging are demonstrated by proposing an overview of the existing applications of averaging for practical switched systems. Examples of power electronics converters, pneumatic actuators and synchronized oscillators are considered. The representation of the different applications by means of a common modeling framework allows to survey the theoretical results of practical interest and to point out some theoretical open issues on the averaging method for switched systems.