Model-matching topics for linear time-varying systems: Computation rules in an algebraic approach

This paper presents implementable solutions to some model-matching type problems for both continuous and discrete-time linear time-varying systems. The parametrization of the whole class of proper solutions to the feedforward exact model-matching problem is given. It is also shown how other control problems can be reduced to the feedforward exact model-matching one. The same approach is used to extend the necessary and sufficient condition for decoupling by precompensation, well known in the time-invariant case, to the time-varying one. The proof is also constructive so that it provides the way to compute the decoupling solution. The approach is algebraic and involves only standard matrix computations which are easily programmable for symbolic computing. Several examples are treated in detail and an industrial application is shown.