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This article considers finite-time bounded controller design for one-sided Lipschitz nonlinear differential inclusions. Sufficient conditions of finite-time bounded criterion are given employing convex hull Lyapunov function approach. An algorithm is designed to calculate the finite-time bounded controller. Moreover, a system initial state selection method is presented to find the domain of system initial state aid for transforming quasi-linear matrix inequality–based conditions to linear matrix inequality-based conditions. Finally, a numerical example and a comparison experiment example are given to illustrate the effectiveness of this proposed design method.

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