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Adaptive Sliding-Mode Control for Perturbed Systems with Zero-Crossing Control Gains

This paper presents a solution to the problem of adaptive sliding-mode control for systems whose control gain presents zero-crossings. The approach is based on the so called barrier function-based adaptive sliding-mode control to avoid the problem of gain over-estimation, while achieving convergence to a predefined neighborhood of the origin. The theoretical properties of the scheme are proven by means of Lyapunov functions and its application to quasi-periodic systems and the problem of orbital stabilization of mechanical systems is demonstrated by means of simulations.