Computation of State Reachable Points of Linear Time Invariant Descriptor Systems

This paper considers the problem of computing the state reachable points, from the origin, of a linear constant coefficient first or higher order descriptor system. A method is proposed that allows to compute 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 differential and algebraic equations while keeping the original state variables. For first order systems 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 an arbitrary point in the reachable set. The results are extended to second order systems and the effectiveness of the proposed approach is demonstrated through some elementary examples.