A stable direct adaptive pole-placer using multisampling and its application to learning control

Using an idea of the periodic control method, this paper proposes a new globally stable direct adaptive pole-placer for a discrete-time multivariable nonminimum-phase system with a priori knowledge of the upper bound on the system observability index. Under periodic control system description, the inverse system representation is first derived to characterize appropriate pole-placing feedback gains and periodic feedback gains in linear equation form suitable for parameter estimation. Then, asymptotic stability of the proposed direct adaptive pole-placer, together with the asymptotic attainment of the desired pole-placement, is established. An application of the proposed scheme to learning control of robots is also considered.