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On the dimension reduction of systems with feedback delay by act-and-wait control

Dimension reduction properties of the act-and-wait controller for systems with feedback delay are analysed. The point of the act-and-wait concept is that the feedback is switched on and off periodically. Earlier works have shown that if the switch-off (waiting) period is longer than the feedback delay, then the system can be described by an n ×n monodromy matrix with n being the dimension of the delay-free system. In this study, it is shown that for certain combinations of the waiting and the acting (or switch on) periods, the system can be still be transformed to a finite, kn-dimensional system with k > 2 even if the waiting period is shorter than the delay. It is shown that the control technique can be a candidate as a solution to the Brockett problem posed for systems with feedback delay.