An energy amplification condition for decentralized adaptive stabilization

The author is interested here in the problem of global decentralized adaptive regulation (of the plant output to zero) of square multivariable linear time-invariant systems without any restrictions on relative degrees or matching assumptions. The first solution to this problem was recently reported by the author using Morse´s new dynamic certainty equivalent adaptive controller to prove that global stabilization is possible if the unmodeled interconnections do not induce “amplification of the energy of the signals in all channels”. In this paper the author shows that to preserve global convergence, it is actually enough to have only one “nonamplifying channel”. Instrumental for the establishment of the authors´ result is the fundamental S-procedure losslessness theorem of Megretsky and Treil, together with some basic loop transformations and D-scalings