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The problem of robust -stability analysis with respect to real convex polytopic uncertainties is tackled. A new ¡ £ ¢ ¥ ¤-based sufficient condition for the existence of parameter-dependent Lyapunov functions is proposed. This condition generalises previously published conditions. Numerical comparisons with quadratic stability results as well as previous results based on parameterdependent Lyapunov functions illustrate the relevance of this new condition. Finally, this result appears to be promising for robust multi-objective performance analysis and control synthesis purposes.