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arXiv · 1807.04481

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

Nicolas Gillis·Michael Karow·Punit Sharma
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Abstract

Consider a discrete-time linear time-invariant descriptor system $Ex(k+1)=Ax(k)$ for $k \in \mathbb Z_{+}$. In this paper, we tackle for the first time the problem of stabilizing such systems by computing a nearby regular index one stable system $\hat E x(k+1)= \hat A x(k)$ with $\text{rank}(\hat E)=r$. 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.

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Nicolas Gillis, Michael Karow, Punit Sharma. 2018-07-12. A note on approximating the nearest stable discrete-time descriptor system with fixed rank. https://doi.org/10.1016/j.apnum.2019.09.004

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