X. Bombois et al., Robustness analysis tools for an uncertainty set obtained by prediction error identification, AUTOMATICA, 37(10), 2001, pp. 1629-1636
This paper presents a robust stability and performance analysis for an unce
rtainty set delivered by classical prediction error identification. This no
nstandard uncertainty set, which is a set of parametrized transfer function
s with a parameter vector in an ellipsoid, contains the true system at a ce
rtain probability level. Our robust stability result is a necessary and suf
ficient condition for the stabilization, by a given controller, of all syst
ems in such uncertainty set. The main new technical contribution of this pa
per is our robust performance result: we show that the worst case performan
ce achieved over all systems in such an uncertainty region is the solution
of a convex optimization problem involving linear matrix inequality constra
ints. Note that we only consider single input-single output systems. (C) 20
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