This paper studies the problems of incremental passivity, incremental passification and incremental stabilization for a switched nonlinear system. First, an incremental passivity concept for switched nonlinear systems is proposed. Each subsystem is only required to be incrementally passive, when it is active. The energy change of each inactive subsystem is charaterized. Then, a sufficient condition for such a system to be incrementally passive is given. Second, a state-dependent switching law and state feedback controllers are designed to render a system with relative degree one incrementally passive. Third, we show that an incrementally passive switched nonlinear system can be incrementally stabilized under some constraints on the energy change of inactive subsystems. In particular, a recursive feedback incremental passification design technique is adopted to achieve the incremental stability for a switched nonlinear system with any same relative degree by designing a set of feedback controllers and a state-dependent switching law, constructively. Finally, two examples are provided to verify the effectiveness of the proposed theory.

中文翻译：

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开关非线性系统的增量无源性和稳定性

本文研究了开关非线性系统的增量无源、增量钝化和增量稳定问题。首先，提出了用于切换非线性系统的增量无源概念。当每个子系统处于活动状态时，它只需要逐渐处于被动状态。表征每个非活动子系统的能量变化。然后，给出了这种系统逐渐被动的充分条件。其次，状态相关的切换律和状态反馈控制器旨在使相对程度为 1 的系统逐渐被动。第三，我们表明，在非活动子系统能量变化的一些约束下，增量无源切换非线性系统可以增量稳定。特别是，采用递归反馈增量钝化设计技术，通过构造性地设计一组反馈控制器和状态相关的切换律，实现任意相对度的切换非线性系统的增量稳定性。最后，提供了两个例子来验证所提出理论的有效性。