Comment on "Adaptive steady-state stabilization for nonlinear dynamical systems".
Instead of the problematic reasoning presented in the work of D. J. Braun [Phys. Rev. E 78, 016213 (2008)], a rigorous argument is provided to show the validity of the adaptive controller proposed by Braun under some particular assumptions. Without these assumptions, this controller may be failed to stabilize the unsteady state, which is numerically shown by specific examples. Also, the choice of parameters to guarantee the validity of these assumptions is illustrated.
Lin
Wei
W
Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China. wlin@fudan.edu.cn