## On computing stabilizability radii of linear time-invariant continuous systems

D. C. Khanh, H. T. Quyen, and D. D. X. Thanh

### Abstract

In this paper we focus on a non-convex and non-smooth singular value optimization problem. Our framework encompasses the distance to stabilizability of a linear system $(A,B)$ when both $A$ and $B$ or only one of them are perturbed. We propose a trisection algorithm for the numerical solution of the singular value optimization problem. This method requires $O(n^4)$ operations on average, where $n$ is the order of the system. Numerical experiments indicate that the method is reliable in practice.

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### Key words

stabilizability radius, optimization, trisection algorithm, linear time-invariant continuous system

### AMS subject classifications

65F15, 93D15, 65K10

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