Detection of limit cycles in discrete systems with backlash and resolution

In this paper, a discretization-oriented describing function is derived for nonlinear devices combining backlash and quantization (resolution) while being subject to discretization through a sampler and zero-order hold. Such a describing function is frequency-dependent so that the overall nonlinearity, which includes both resolution and backlash, is interpreted as one possessing nonlinear inertia. That inertia is generated by the sampling process since it does not appear if the system is continuous. The presence of limit cycles is investigated through simulated examples.<
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