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In this paper, we consider the problem of computing the nearestuncontrollable (C-uncontrollable) system to a given higher order system. Thedistance to the nearest uncontrollable system, also termed as the radius ofcontrollability, is a good measure of gauging the numerical robustness of thegiven system with respect to controllability. Here, we invoke the equivalenceof C-controllability of a higher order system with full rank property of acertain Toeplitz structured matrix. This enables us to pose the problem ofcomputing the radius of controllability as equivalent to the problem ofcomputing the nearest structured low rank approximation of this Toeplitzstructured matrix. Through several numerical examples and comparison with thebenchmark numerical problem, we illustrate that our approach works well.

Structured real radius of controllability for higher order LTI systems