Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots
Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots
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DOI：
10.1109/tac.2008.923688
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发表时间：
2008-08
影响因子：
6.8
通讯作者：
Ti-Chung Lee;Zhong-Ping Jiang
中科院分区：
文献类型：
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作者：
Ti-Chung Lee;Zhong-Ping Jiang
本文研究一般非线性时变切换系统的局部和全局一致渐近稳定性。引入了两个李雅普诺夫函数的概念，并利用它们建立了一致李雅普诺夫稳定性和一致全局稳定性。借助于输出函数，提出了一个几乎有界的输出能量条件和一个输出持续激励条件，并用于保证系统的一致局部和全局渐近稳定性.在此基础上，给出了Krasovskiii-LaSalle定理在时变切换系统中的推广形式.对于具有持续驻留时间的切换系统，在零状态可观测性条件下，保证了输出持续激励条件成立。它表明，在过去的文献中的几个现有的结果可以覆盖作为特殊情况下，使用所提出的标准。有趣的是，与以前的工作相反，本文的主要结果适用于某些切换系统在原点不渐近稳定的情况。非完整移动的机器人的鲁棒实际调节问题的研究，作为一种方式来证明所提出的新标准的权力。针对移动的机器人，提出了一种对姿态误差和未知参数具有鲁棒性的切换控制器。
This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability. Based on this result, a generalized version of Krasovskii-LaSalle theorem in time-varying switched systems is proposed. For switched systems with persistent dwell-time, the output persistent excitation condition is guaranteed to hold under a zero-state observability condition. It is shown that several existing results in past literature can be covered as special cases using the proposed criteria. Interestingly, as opposed to previous work, the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin. The robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria. A novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots.