document: Closed-loop model set validation under a stochastic framework Deals with probabilistic model set validation . It is assumed that the dynamics of a multi-input multi-output -LRB- MIMO -RRB- plant is described by a model set with unstructured uncertainties , and identification experiments are performed in closed loop . A necessary and sufficient condition has been derived for the consistency of the model set with both the stabilizing controller and closed-loop frequency domain experimental data -LRB- FDED -RRB- . In this condition , only the Euclidean norm of a complex vector is involved , and this complex vector depends linearly on both the disturbances and the measurement errors . Based on this condition , an analytic formula has been derived for the sample unfalsified probability -LRB- SUP -RRB- of the model set . Some of the asymptotic statistical properties of the SUP have also been briefly discussed . A numerical example is included to illustrate the efficiency of the suggested method in model set quality evaluation
doc_bio_tags: O O O O O O B I O O B I I I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I I I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O