paper

A note on approximating the nearest stable discrete-time descriptor system with fixed rank

arXiv:1807.04481 · doi:10.1016/j.apnum.2019.09.004

Abstract

Consider a discrete-time linear time-invariant descriptor system $E x (k + 1) = A x (k)$ for $k \in Z_{+}$ . In this paper, we tackle for the first time the problem of stabilizing such systems by computing a nearby regular index one stable system $E^x (k + 1) = A^x (k)$ with $rank (E^) = r$ . We reformulate this highly nonconvex problem into an equivalent optimization problem with a relatively simple feasible set onto which it is easy to project. This allows us to employ a block coordinate descent method to obtain a nearby regular index one stable system. We illustrate the effectiveness of the algorithm on several examples.

10 pages, 3 tables, 1 figure