We are interested inH∞synthesis conditions for Linear Parameter Varying (LPV) filter design. We prove that an existing class of sufficient conditions for poly-quadraticH∞filter synthesis is in fact necessary as well. We develop alternative conditions based on a new theory of duality for poly-quadratic Lyapunov functions. We use these results to show how poly-quadraticH∞state feedback synthesis conditions can be used for poly-quadraticH∞LPV filter synthesis.
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