Lyapunov-based adaptive control of MIMO systems

The design of model-reference adaptive control (MRAC) for MIMO linear systems has not yet been achieved, in spite of significant efforts, the completeness and simplicity of its SISO counterpart. One of the main obstacles has been the generalization of the SISO assumption that the sign of the high-frequency gain is known. Here we overcome this obstacle and present a MIMO analog to the well known Lyapunov-based MRAC SISO design. Our algorithm makes use of a new control parametrization derived from a factorization of the high-frequency gain matrix K_p =SDU, where S is symmetric positive definite, D is diagonal, and U is unity upper triangular. Only the signs of the entries of D or, equivalently, the signs of the leading principal minors of K_p, are assumed to be known