Normalised quadratic control, a modification of the conventional quadratic control method has recently been proposed to exponentially stabilise a homogeneous bilinear system wliose open-loop eigcnvalucs all fall on the imaginary axis. The normalised quadratic control method is now extended to a broader class of bilinear systems whose open-loop eigenvalues may fall to the left or right of the imaginary axis. It is shown that for bilinear systems that are already open-loop stable. the normalised quadratic control can add to the system an extra exponcntial decay rate. For open-loop unstable bilinear systems. the normalised quadratic control can stabilise the system if the extra exponcntial decay rate provided by the control is larger than the open-loop system's growth rate.
We explore in this paper the efficient clustering of item data. Different from those of the traditional data, the features of item data are known to be of high dimensionality and sparsity. In view of the features of item data, we devise in this paper a novel measurement, called the associationtaxonomy similarity, and utilize this measurement to perform the clustering. With this association-taxonomy similarity measurement, we develop an efficient clustering algorithm, called algorithm AT (standing for Association-Taxonomy), for item data. Two validation indexes based on association and taxonomy properties are also devised to assess the quality of clustering for item data. As validated by the real dataset, it is shown by our experimental results that algorithm AT devised in this paper significantly outperforms the prior works in the clustering quality as measured by the validation indexes, indicating the usefulness of association-taxonomy similarity in item data clustering.
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