ON NECESSARY ASSUMPTIONS IN DISCRETE-TIME MODEL-REFERENCE ADAPTIVE-CONTROL

In this paper we investigate the discrete-time model reference adaptiv e control problem, ascertain the extent to which the classical assumpt ions are necessary and provide several suitably modified inviolable re quirements. 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 di sc lie in a finite set. We also derive a bound on the achievable asymp totic performance in the event that these requirements are not met.