On necessary assumptions in discrete‐time model reference adaptive control

Abstract

In this paper we investigate the discrete-time model reference adaptive control problem, ascertain the extent to which the classical assumptions are necessary and provide several suitably modified inviolable requirements. In particular, we show that under a closed-loop causality constraint the problem is solvable only if there is an upper bound on the plant relative degree and the plant zeros outside the open unit disc lie in a finite set. We also derive a bound on the achievable asymptotic performance in the event that these requirements are not met.