The paper presents a parameter-dependent Lyapunov approach for the control of nonstationary linear-parameter varying systems. The work is motivated by the challenges encountered in controlling nonlinear systems about pre-specified aggressive trajectories, specifically ones which eventually settle into periodic orbits. The control design method uses the l(2)-induced norm performance measure, and the analysis and synthesis results are given in terms of parameterized linear matrix inequalities. Two fast and easy-to-implement algorithms for online controller construction are also provided.