Adaptive and non-adaptive "pole-placement" control of multivariable linear time-varying plants

In this paper we address the adaptive and nonadaptive "pole-placement" control problem for a class of index-invariant linear time-varying multivariable plants. We show that, in the case where the plant parameters are completely known, a "pole-placement" like control algorithm can be designed by solving a time-varying Diophantine equation. Further, we show that 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, we employ a gradient-based adaptive law with projection and normalization to estimate the plant parameters online and then design the controller based on these parameter estimates and establish the stability properties of the adaptive closed-loop plant.