## New methods for estimating the distance to uncontrollability.(English)Zbl 0954.65056

Given a linear time-invariant control system, the author presents new algorithms intended to estimate the distance to uncontrollability, i.e. the norm of the smallest perturbation that makes the given system uncontrollable. At the core of these algorithms is the computation of all real eigenvalues of a sparse $$4n^2\times 4n^2$$ eigenvalue problem. The algorithms are claimed to be the first that correctly estimate the distance to uncontrollability at a cost which is a polynomial in the dimension of the given system. Results from some numerical experiments that demonstrate the reliability and effectiveness of the algorithms are reported.

### MSC:

 65K10 Numerical optimization and variational techniques 93B05 Controllability 65F05 Direct numerical methods for linear systems and matrix inversion 93B40 Computational methods in systems theory (MSC2010)

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