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In this paper, we derive several new criteria for the - Instability of large-scale interconnected systems. These fall into two categories: the first set of results is based on the idea of dissipativity, while the second set is based on an orthogonal decomposition of the input space. The latter results have the advantage that they can be readily converted into -instabiity criteria using the technique of exponential weighting. The former results are more general, but provide only -instability criteria and no -instability criteria.