Internal exponential stabilization to a nonstationary solution for 1D Burgers equations with piecewise constant controls

The feedback stabilization of the Burgers system to a nonstationary solution using a finite number of internal piecewise constant controls is considered. Estimates for the number of needed controls are derived. In the particular case of no constraint on the support of the control a better estimate is derived, so the possibility of getting an analogous estimate for the general case is discussed. That possibility is suggested by the results of some numerical simulations.