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An innovative method for robust stability analysis of dynamic systems with interval time-varying delay and uncertainties of structural and polytopic types is proposed. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov function. The stability criteria derived from this method significantly improves and simplifies the existing stability conditions obtained through employing the technique with the least number of Linear matrix inequality variables. The simplicity of the stability criteria results from the fact that neither any useful terms are ignored in dealing with cross-product terms nor any superfluous free weighting matrices are introduced in the theoretical derivation. Numerical examples are given to demonstrate the effectiveness of the proposed method.