Adaptive and non-adaptive 'pole-placement' control of multivariable lineartime-varying plants

In this paper, the adaptive and non-adaptive 'pole-placement' control probl ems 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 designe d by solving a time-varying Diophantine equation. Furthermore, the tracking performance of such a controller can be improved by incorporating the inte rnal model principle into the design. In the case where the plant parameter s are only partially known, a gradient-based adaptive law with projection a nd normalization is employed to estimate the plant parameters on-line. An a daptive controller is then designed, based on these parameter estimates, an d the stability properties of the adapt ive closed-loop plant are establish ed. The design and realization of both the adaptive and non-adaptive contro l laws is illustrated by means of a simple example.