Global Adaptive Pole Positioning

Adaptive pole positioning for linear time-invariant discrete time systems is considered, under the constraint that the controller consists of an identifier, the gains in which do not go to zero, an observer, and a state feedback law (the latter two elements being viewed in transfer function form). A globally convergent algorithm is presented for achieving a prescribed set of closed-loop poles. Persistency of excitation of an external input is required, together with an underbound on the magnitude of the Sylvester resultant of the plant numerator and denominator polynomials, this in effect being an underbound on the product of a measure of pole-zero separation and a generalized gain.