Act-and-wait control concept for discrete-time systems with feedback delay

Linear n-dimensional discrete-time systems are considered with feedback delay r at the m-dimensional input. These systems have n + mr poles. The act-and-wait control concept is introduced: the feedback is periodically switched on and off during the control with period k. It is switched on for one step (act) and switched off for (k - 1) number of steps (wait). It is shown that if the act-and-wait period is larger than the time delay (i.e. k > r), then mr poles of the system are equal to zero, and the remaining poles can be placed arbitrarily if the system matrices satisfy certain controllability conditions.