On the projection algorithm and delay of peaking in adaptive control

Adaptive deadbeat control is considered for the deterministic linear plant without any persistent excitation assumption imposed. The upper bound on the rate of convergence is provided for the control algorithm that uses the projection identification algorithm. On the other hand, it is shown that convergence is delayed if the regularized identification algorithm is used. It is shown that arbitrarily large delays can precede an overshoot under certain choices of initial conditions. An estimate is also provided for the amplitude of the peak