This paper presents a model reference adaptive control scheme for
deterministic continuous-time multivariable systems represented by
square, strictly proper, minimum-phase transfer function matrices. A
typical requirement of existing algorithms is to assume that the zero
structure at infinity and the high-frequency gain matrix are fully (or
at least partially) known. It is well known that these requirements
may be very restrictive, since in general both the zero structure at
infinity and the high-frequency gain matrix depend on plant
parameters.
In this paper we show that these restrictive assumptions may be
considerably weakened using a hysteresis switching control
strategy recently introduced by Morse et~al. The strategy entails
running a finite number of parameter estimators in parallel, and using
a switching algorithm to select between candidate estimators based on
their associated prediction errors. Hysteresis in the switching
algorithm precludes switching arbitrarily rapidly between estimators,
and all switching ceases within a finite time.
The results represent a significant step forward in understanding the
minimal amount of prior knowledge necessary to design a stabilizing
controller for a linear multivariable system.