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 like a reference model in response to an exogenous input. Conditions for solvability via a linear time-invariant controller are well known; here we prove that under a closed-loop causality constraint, moving to a nonlinear time-varying controller affords no reduction of these conditions. We explore the ramifications of this result to the (ideal) model reference adaptive control problem, demonstrating that (i) an upper bound on the plant relative degree must be known, and (ii) the plant zeros 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 that the solvability conditions fail to hold. [ABSTRACT FROM AUTHOR]