Semi-discretization and the time-delayed PDA feedback control of human balance

An important question for human balance control concerns how the differential equations for the neural control of balance should be formulated. In this paper, we consider a discrete-time and a continuous-time delayed proportional-derivative-acceleration controller and establish the transition between them by means of the semi-discretization. We show that the critical delay, which limits stabilizability of the system, is about the same for the continuous-time systems and its semi-discrete counterparts.