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Improved signal synthesis techniques are developed for nonlinear, time-varying systems having unspecified plant parameters lying within known bounds. Output system errors satisfy a Lyapunov stability theorem which guarantees that they approach zero asymptotically. Improved results are derived first by using a quadratic-form Lyapunov function of system errors and then by using expanded Lyapunov functions involving derivatives of system errors to yield smoother input adaptive signals for a broad class of systems. An example is provided to illustrate the indicated design improvements.