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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 l2-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.