This paper is concerned with the problem of full-order H2 and H∞ linear parameter varying filter design for continuous-time systems with arbitrarily time-varying parameters. The time-varying parameters belong to a polytope with known vertices, affect all the system matrices and are assumed to be available online for implementation of the filters. The synthesis conditions are formulated in terms of parameter dependent Linear Matrix Inequalities (PDLMIs). A sequence of standard LMI conditions assuring the existence of homogeneous polynomially parameter-dependent (HPPD) solutions to the parameter-dependent LMIs for filter design is provided in terms of the vertices of the polytope yielding parameter dependent filters of arbitrary degree assuring quadratic stability of the error dynamics. By definition of slack variables, extra free dimensions are provided to the parameter dependent filter design optimization problem, so method presented in this paper expected to be less conservative than the existing methods for the polytopic uncertain systems and efficiency of the method for filter design is illustrated by means of numerical comparisons with some benchmark examples from the literature.