This paper proposes a new model-based control for flexible-link robots based on Lyapunov stability theorem, where a V-shape Lyapunov function is introduced for the flexible robot dynamics that do not satisfy the so-called matching condition. First, a new model-based nonlinear control is proposed based on a V-shape Lyapunov function, where the global exponential stability of the control is obtained. The model-based control is then extended to a model-based adaptive control to cope with parametric uncertainties in the dynamics, where the global asymptotic stability of the control is attained. The effectiveness of the proposed approach has been shown by computer simulation.

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