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In this paper a new LMI method is proposed for the strong γk-γcl H∞ stabilization problem. Due to the introduction of a new slack variable, it is expected to be less conservative than the authors' previous work. Furthermore, several recently developed methods can be seen as its special cases. Meanwhile the extended bounded real lemma proposed lately can be adopted to improve the LMI design results iteratively. And for the possible order problem, the nested construction method can also be applied. The effectiveness is demonstrated by two numerical examples.