Analysis of almost-everywhere stability of a class of discontinuous systems via Lyapunov densities
Analysis of almost-everywhere stability of a class of discontinuous systems via Lyapunov densities
复制标题
通过李雅普诺夫密度分析一类不连续系统的几乎处处稳定性
DOI：
10.1109/ecc.2016.7810345
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Izumi Masubuchi and Yuzo Ohta
中科院分区：
文献类型：
--
作者：
Yoichiro Iwasaki;Masato Misumi;Toshiyuki Nakamiya;Izumi Masubuchi and Yuzo Ohta
非线性系统稳定性分析的李雅普诺夫密度方法已被推广到包括状态反馈增益综合在内的各种问题。然而，大多数现有的结果假设非线性系统的向量场的光滑性，这是必不可少的利用沿沿着轨迹的系统的测量的导数。与以往的结果不同，本文在适定性的假设下，给出了一类分段光滑间断系统几乎处处稳定的Lyapunov密度条件.所提出的条件包括由一个李雅普诺夫密度及其导数的向量场的可微点和一个条件上的向量场的不连续的表面上的措施给出的积极性。
Methods of Lyapunov densities for stability analysis of nonlinear systems have been extended to various problems including synthesis of state feedback gains. However, most of the existing results assume smoothness of the vector field of nonlinear systems, which is essential to utilize derivative of measures along the trajectories of the system. Unlike such previous results, this paper provides a Lyapunov-density condition for almost-everywhere stability of a class of piecewise smooth discontinuous systems under some assumptions on well-posedness. The proposed condition consists of positivity of the measure given by a Lyapunov density and its derivative on the differentiable points of the vector fields and a condition on the surfaces of discontinuity of the vector field.