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_m: a matrix S_m must be known such that B_mS_m=(B_mS_m)^T>0. In this paper, using the SDU factorization of B_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_m, are assumed to be known.