ON ASYMPTOTIC MODEL-MATCHING

In this paper we consider the problem of asymptotic model matching, in which the objective is to force the plant to behave asymptotically li ke a reference model in response to an exogenous input. Conditions for solvability via a linear time-invariant controller are well known; he re we prove that under a closed-loop causality constraint, moving to a nonlinear time-varying controller affords no reduction of these condi tions. We explore the ramifications of this result to the (ideal) mode l reference adaptive control problem, demonstrating that (i) an upper bound on the plant relative degree must be known, and (ii) the plant z eros in the closed right half-plane must lie in a finite set. We also derive a bound on the achievable asymptotic performance in the event t hat the solvability conditions fail to hold.