论文标题
某些非线性时间变化系统的捕获/稳定区域的稳定性和估计的稳定性和估计
Solution Bounds, Stability and Estimation of Trapping/Stability Regions of Some Nonlinear Time-Varying Systems
论文作者
论文摘要
在众多工程，自然科学和控制问题中，对时间依赖的非线性系统的解决方案规范和稳定性的估计无处不在。但是，实际上有价值的结果在这方面很少见。本文开发了一种新的方法，该方法界定了解决方案规范，得出了相应的稳定性标准，并估算了某些非自主和非线性系统的陷阱/稳定性区域，这些区域在各种应用域中出现。我们的推论在于为初始系统的解决方案规范得出标量差异不平等。 Lipschitz不等式的效用使相关的辅助微分方程线性化，并获得了解决方案规范和相关稳定性标准的上限。为了完善这些推论，我们引入了Lipschitz不平等的非线性扩展，该扩展改善了开发的界限并允许估算相应系统的稳定性盆地和捕获区域。最后，我们在代表性模拟中确认了理论结果。
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which bounds the solution norms, derives the corresponding stability criteria, and estimates the trapping/stability regions for some nonautonomous and nonlinear systems, which arise in various application domains. Our inferences rest on deriving a scalar differential inequality for the norms of solutions to the initial systems. Utility of the Lipschitz inequality linearizes the associated auxiliary differential equation and yields both the upper bounds for the norms of solutions and the relevant stability criteria. To refine these inferences, we introduce a nonlinear extension of the Lipschitz inequality, which improves the developed bounds and allows estimation of the stability basins and trapping regions for the corresponding systems. Finally, we confirm the theoretical results in representative simulations.
