Modal Control and Stabilization of Linear Periodic Object with Low Frequency Pulse Controller

The report considers a closed system
$S_{d}$
, consisting of a linear continuous periodic object having a period
$T$
, and an impulse regulator functioning with a quantization period
$T_{d}=dT$
, where
$d > 1$
is an integer. On the basis of the theory of determinant polynomial equations, the necessary and sufficient conditions for the modal controllability of the system
$S_{d}$
are obtained. In the absence of modal controllability, necessary and sufficient conditions for the stabilisability of the system
$S_{d}$
are given.