In this paper, a new approach for linear parameter-varying (LPV) system analysis and control synthesis is proposed. This unified framework combines two seemingly diversified methods in systematic gain-scheduling, LPV control theory, and extends the applicability of full block S-procedure to a general class of LPV systems. An example is used to demonstrate the proposed general LPV design approach, and to show its relative merits compared to other systematic gain-scheduling control techniques.