We study stability of multivariable control-affine nonlinear systems under sparsification of feedback controllers. Given a stabilizing feedback, sparsification in our context refers to the scheduling of the individual control inputs one at a time in rapid periodic sweeps over the set of control inputs, which corresponds to round-robin scheduling. We prove that if a locally asymptotically stabilizing feedback controller is sparsified via the round-robin scheme and each control action is scaled appropriately, then the corresponding equilibrium of the resulting system is stabilized when the scheduling is sufficiently fast; under mild additional conditions, local asymptotic stabilization of the corresponding equilibrium can also be guaranteed. Moreover, the basin of attraction for the equilibrium of scheduled system also remains the same as the original system under sufficiently fast switching Our technical tools are derived from optimal control theory, and our results also contribute to the literature on the stability of switched systems in the fast switching regime. Illustrative numerical examples depicting several subtle features of our results are included.

我们研究了稀疏化下多变量控制仿射非线性系统的稳定性 反馈控制器。给定一个稳定的反馈，在我们的上下文中，稀疏化是指在对控制输入集的快速周期性扫描中一次一个地调度单个控制输入，这对应于循环调度。我们证明，如果一个局部渐近稳定的反馈控制器通过循环方案被稀疏化，并且每个控制动作都被适当地缩放，那么当调度足够快时，结果系统的相应平衡是稳定的；在温和的附加条件下，也可以保证相应平衡的局部渐近稳定。而且，在足够快的切换下，调度系统平衡的吸引力盆地也保持与原始系统相同我们的技术工具源自最优控制理论，我们的结果也有助于快速切换中切换系统稳定性的文献政权。包括描述我们结果的几个微妙特征的说明性数字示例。