A Result on the Placement of Infinite Eigenvalues in Descriptor Systems

It is known that under certain circumstances the trajectories of the descriptor system Ex(t) = Ax(t) + Bu(t) will involve the impulse function and its derivatives. Although a feedback can effectively be designed to eliminate this behavior, it may destablize the system or destroy its regularity. In this paper we present a straightforward way to choose the feedback such that these problem do not occur. Since elimination of impulsive behavior is closely related to shifting the eigenvalues at infinity of the system to the finite portion of the complex plane, our result can also be thought of as a pole-placement theorem for the eigenvalues at infinity of a descriptor system.