In this paper, we consider the stabilization of & nbsp;phi(t)-a(0)phi(t)=-k(p)phi(t-tau-delta(p))-k(d)phi(t-tau-delta(d))-k(a)phi(t-tau-delta(a)),&
nbsp;which describes the control of an & nbsp;inverted pendulum & nbsp;by detuned
proportional-derivative-acceleration (PDA) feedback. We show that the system can be
stabilized using an appropriate choice of the control parameters & nbsp;k(p),& nbsp;k(d),&
nbsp;k(a)& nbsp;and & nbsp;delta(p),& nbsp;delta(d),& nbsp;delta(a)& nbsp;>= 0 & nbsp;if
& nbsp;tau & nbsp;is smaller than the critical delay & nbsp;tau(crit)=root 6/a(0).
This value is larger by a factor of & nbsp;root 3 asymptotic to 1.73 & nbsp;than the
critical delay of the proportional-derivative (PD) feedback with a single delay.
