Design of controllers for hybrid linear systems with impulsive inputs and periodic jumps

In this study, the problem of designing a controller for a hybrid system with impulsive input and periodic jumps is addressed. In particular, it is shown that any hybrid system with impulsive inputs and periodic jumps can be recast into a discrete-time, linear, time-invariant system, which, in turn, can be used to design a controller by using classical methods. Furthermore, it is shown that, once such a controller has been designed, it can be readily used to control the hybrid system by mean of an interfacing system that is based just on the continuous-time dynamics of the plant to be controlled. Several examples, spanning from aerospace to biomedical applications, are reported in order to corroborate the theoretical results.