Model reference adaptive and non-adaptive control of multivariable linear time-varying plants: the exact matching case

In this paper we address the adaptive and non-adaptive model reference control problem for a class of linear time-varying plants, namely the index-invariant ones. We show that, under appropriate controllability and observability conditions, this class of plants admits a fractional description in terms of polynomial differential operators and, as such, allows for a polynomial equation-based controller design. We also show that, for a control objective of the model reference type, the controller can be designed by solving a set of algebraic equations. Further, in the case where the plant parameters are only partially known, we employ a gradient-based adaptive law with projection and normalization to update the controller parameters and establish the stability and tracking properties of adaptive closed-loop plant.