Adaptive backstepping control design for MIMO plants using factorization

The generalization of the adaptive backstepping control for linear MIMO plants made a restrictive assumption about the high frequency gain B/sub m/: a matrix S/sub m/ must be known such that B/sub m/S/sub m/=(B/sub m/S/sub m/)/sup T/>0. In this paper, using the SDU factorization of B/sub m/, where S is symmetric positive definite, D is diagonal, and U is unity upper triangular, we eliminate that restrictive assumption introducing a new MIMO adaptive backstepping algorithm, where only the signs of the entries of D or, equivalently, the signs of the leading principal minors of B/sub m/, are assumed to be known.