An equivalence between fast periodic-switched systems and time-invariant systems

It is shown that a certain class of linear systems with constant parameters and periodically operated switches can be approximated by a linear time-invariant system provided that the switching frequency is much greater than the magnitude of the largest natural frequency of the linear time-invariant system. Furthermore, a special type of switching allows the linear time-invariant system to be frequency scaled by simply varying the average value of the switching function. This feature allows one to design electronically tunable filters.