The stability robustness determination of state space models with real unstructured perturbations |
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Authors: | L Qiu E J Davison |
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Affiliation: | (1) Department of Electrical Engineering, University of Toronto, M5S 1A4 Toronto, Ontario, Canada |
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Abstract: | This paper considers the robust stability of a linear time-invariant state space model subject to real parameter perturbations.
The problem is to find the distance of a given stable matrix from the set of unstable matrices. A new method, based on the
properties of the Kronecker sum and two other composite matrices, is developed to study this problem; this new method makes
it possible to distinguish real perturbations from complex ones. Although a procedure to find the exact value of the distance
is still not available, some explicit lower bounds on the distance are obtained. The bounds are applicable only for the case
of real plant perturbations, and are easy to compute numerically; if the matrix is large in size, an iterative procedure is
given to compute the bounds. Various examples including a 46th-order spacecraft system are given to illustrate the results
obtained. The examples show that the new bounds obtained can have an arbitrary degree of improvement over previously reported
ones.
This work has been supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A4396. |
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Keywords: | Robust stability Real unstructured perturbations Stability radius Composite matrices State space models |
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