Robustness of the adaptive backstepping controllers for linear systems

We present a unified procedure for designing and analyzing robust adaptive backstepping controllers for linear systems. Both the modular design and tuning functions design are considered. These controllers guarantee global signal boundedness and small tracking error of the order of the modeling error, in the presence of a general class of multiplicative unmodeled dynamics. It is shown that the modular design results in a linear controller which has the same robustness properties as the traditional certainty-equivalence based linear adaptive controllers. The tuning functions design, however, gives a nonlinear controller, whose robustness property in terms of the class of allowable unmodeled dynamics, is relatively weaker