Sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and application to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e568" altimg="si4.svg"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> filtering for linear systems with time-varying delays

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