The H-infinity filtering problem for continuous-time linear systems with polytopic uncertainty is addressed in this study. First, using several well-known lemmas from the literature, adequate analysis requirements in terms of linear matrix inequalities (LMIs) are developed, ensuring the asymptotic stability of the filtering error systems with the specified H-infinity performance level gamma. We will then concentrate on the design of filter gains using less restricted LMIs by combining several strategies that utilize slack variables and descriptor representation. Finally, numerical examples are presented to demonstrate the efficacy of the suggested technique in contrast to current works.