Computation of state reachable points of descriptor systems

This paper considers the problem of computing the state reachable points, from the origin, of a linear constant coefficient descriptor system. A numerical algorithm is proposed that can be implemented to characterize the reachable set in a numerically stable way. The original descriptor system is transformed into a strangeness-free system within the behavioral framework followed by a projection that separates the system into its differential and algebraic parts. It is shown that the computation of the image space of two matrices, associated with the projected system, is enough to compute the reachable set (from the origin). Moreover, a characterization is presented of all the inputs by which one can reach to any arbitrary points in the reachable set. The effectiveness of the proposed approach is demonstrated through numerical examples.