Actual systems have input constraints due to the performances of actuators and the protections of control systems. For input constrained nonlinear systems, several controllers based on control Lyapunov functions are proposed. In this paper, we introduce Kidane's controller to discontinuous nonlinear systems with input contraints and prove that the asymptotic stability and the inverse optimality of controlled systems are guaranteed. We propose a combined controller which achieves both the

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... domain of attraction and the inverse optimality under the input constraint. Finally, we apply the controller to a single-link robot arm and confirm the effectiveness of the proposed method by computer simulation and experiments.