Multivariable Adaptive Backstepping Control: A Norm Estimation Approach

In this note, a novel output-feedback adaptive backstepping control is proposed for linear time-invariant multivariable plants under a mild assumption that the Hurwitz condition for high-frequency gain matrix is satisfied. By estimating the norm of those unknown parameter matrices instead of their elements, it is shown that only one parameter needs to be updated online and therefore, the computational burden can be greatly reduced compared with any current multivariable adaptive control scheme.