The Implicit Lyapunov Function (ILF) for a class of homogeneous systems is introduced and studied. The analysis of homogeneous differentiator using ILF method is presented. Sufficient stability conditions for homogeneous differentiator are obtained and represented by a parameterized system of Linear Matrix Inequalities (LMI). The differentiation error and convergence time are estimated. The procedure of parameters tuning for homogeneous differentiator is formulated as the semi-definite programming problem with LMI constraints. The obtained theoretical results are supported by numerical simulations.