In this paper, the adaptive and non-adaptive 'pole-placement' control problems are addressed for a class of index-invariant multivariable linear time-varying plants. In the case where the plant parameters are completely known, it is shown that a 'pole-placement'-like control algorithm can be designed by solving a time-varying Diophantine equation. Furthermore, the tracking performance of such a controller can be improved by incorporating the internal model principle into the design. In the case where the plant parameters are only partially known, a gradient-based adaptive law with projection and normalization is employed to estimate the plant parameters on-line. An adaptive controller is then designed, based on these parameter estimates, and the stability properties of the adapt ive closed-loop plant are established. The design and realization of both the adaptive and non-adaptive control laws is illustrated by means of a simple example.