Singularly Perturbed Derivative Coupling-Filter

Abstract In some control and observations problems, it may be convenient, at least from the analysis point of view, to use non proper systems. However, as far as their implementation is concerned, proper approximations have to be designed. In this paper, we show how exponential approximations can be rather easily designed. We consider the MIMO case and study the relative stability of the approximation. As a by product, we show that the set of proper time-invariant linear systems is dense in the set of regular linear descriptor systems.