论文标题
在非线性系统的输入延迟下设置输入到州的稳定性
Set input-to-state stability under input delays for nonlinear systems with disturbances
论文作者
论文摘要
该研究提出了针对固定的稳定性（ISS）的新结果，但要经过较小的输入时间延迟，即紧凑，不变的集合包含原点。首先，使用非线性小增益理论，我们证明了一种razumikhin型定理，该定理可确保在功能微分方程（FDES）设置中的ISS具有干扰。接下来，我们显示该定理如何用于确保具有输入延迟和干扰的非线性系统的ISS设置。与在输入中相对于较小时间延迟的现有ISS鲁棒性的现有研究相比，我们的结果相当广泛，保留了ISS的收益，并且在时间延迟状态下没有任何限制。该方法的有效性是通过两个案例研究来说明的，这些案例研究解决了实践感兴趣的非线性振荡器类别的设定稳定性。
The study proposes new results on the set input-to-state stability (ISS) subject to a small input time delay for compact, invariant sets that contains the origin. First, using the nonlinear small-gain theory, we prove a Razumikhin-type theorem that ensures ISS for sets in the setup of functional differential equations (FDEs) with disturbances. Next we show how this theorem can be used to ensure set ISS for nonlinear systems with input delays and disturbances. In comparison to the existing research on set ISS robustness with respect to small time delays at the input, our results are rather broad, retaining the ISS gain and without any constraints on time delayed states. The effectiveness of the method is illustrated through two case-studies addressing set stability for classes of nonlinear oscillators of practical interest.
