On Uniform Global Asymptotic Stability of Nonlinear Discrete-Time Systems With Applications
On Uniform Global Asymptotic Stability of Nonlinear Discrete-Time Systems With Applications
复制标题
非线性离散时间系统的一致全局渐近稳定性及其应用
DOI：
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发表时间：
2006
影响因子：
6.8
通讯作者：
Zhong
中科院分区：
文献类型：
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作者：
T. Lee;Zhong
本文提出了非线性和时变离散时间系统的一致全局渐近稳定性的新特征。在温和的假设下，结果表明，弱零状态可检测性相当于全局一致稳定系统的一致全局渐近稳定性。通过采用简化限制系统的概念，基于与原始系统相关的简化限制系统的可检测性，提出了均匀全局渐近稳定性的另一个表征。作为副产品，我们针对一般时变系统（不一定是周期性系统）导出了著名的克拉索夫斯基-拉萨尔定理的广义离散时间版本。此外，我们应用所获得的稳定性结果来分析级联时变系统的一致渐近稳定性，并表明可以放宽最近论文中的一些技术假设。通过实际应用，我们的结果表明，我们的结果在保证吸引力方面与经典的拉萨尔不变性原理发挥了类似的作用，注意到使用了简化的限制系统而不是原始系统。为了验证概念特征，我们通过精确的离散时间模型而不是近似模型来研究非完整移动机器人基准示例的采样数据稳定性问题。该案例研究还表明，一般来说，采样数据系统可能会变得非周期性，即使其原始连续时间系统是周期性的。使用新的稳定性结果提出了一种新颖的采样数据稳定器设计，并通过仿真结果得到支持
This paper presents new characterizations of uniform global asymptotic stability for nonlinear and time-varying discrete-time systems. Under mild assumptions, it is shown that weak zero-state detectability is equivalent to uniform global asymptotic stability for globally uniformly stable systems. By employing the notion of reduced limiting systems, another characterization of uniform global asymptotic stability is proposed on the basis of the detectability for the reduced limiting systems associated with the original system. As a by-product, we derive a generalized, discrete-time version of the well-known Krasovskii-LaSalle theorem for general time-varying, not necessarily periodic, systems. Furthermore, we apply the obtained stability results to analyze uniform asymptotic stability of cascaded time-varying systems, and show that some technical assumptions in recent papers can be relaxed. Through a practical application, it is shown that our results play a similar role to the classic LaSalle invariance principle in guaranteeing attractivity, noting that reduced limiting systems are used instead of the original system. To validate the conceptual characterizations, we study the problem of sampled-data stabilization for the benchmark example of nonholonomic mobile robots via the exact discrete-time model rather than approximate models. This case study also reveals that in general, sampled-data systems may become non-periodic even though their original continuous-time system is periodic. A novel sampled-data stabilizer design is proposed using the new stability results and is supported via simulation results