Pole placement in non connected regions for descriptor models

This paper proposes a method to compute a static state feedback control law which achieves a non strict pole assignment on a continuous or a discrete descriptor system. The specification on the closed-loop poles is given in terms of D-stability, i.e. in terms of a pole-clustering region D. In this work, the clustering region is possibly non path-connected since it can result from the union of disjoint and non symmetric subregions. Such a choice, which is original when the design of linear descriptor systems is concerned, is made possible by a technique that enables a partial pole placement via aggregation. The distribution of the finite poles in various subregions can be chosen. Some key steps of the procedure are addressed through strict LMI (Linear Matrix Inequalities). This is an extension of a previous work from conventional to descriptor models. Therefore, not only stability is to be ensured but also, because of infinite poles, regularity and causality or impulse freeness (the whole of those properties being termed admissibility).