Structural stability of singular systems under proportiona and derivative feedback

Abstract

We consider triples of matrices (E; A;B), representing singular linear time in- variant systems in the form Ex_ (t) = Ax(t) + Bu(t), with E;A 2 Mp£n(C) and B 2 Mn£m(C), under proportional and derivative feedback. In this work we study the equivalence relation considered, as a Lie group action that permit us to see the equivalence classes as di®erentiable manifolds. The description of the tangent and normal space to the orbits permits us to give a characterization of the structural stability of triples of matrices, in terms of numerical invariants.