一类广义Hamilton系统的有限时间稳定性及其在仿射非线性系统控制设计中的应用

山东大学学报(工学版) ›› 2011, Vol. 41 ›› Issue (2): 119-125.

一类广义Hamilton系统的有限时间稳定性及其在仿射非线性系统控制设计中的应用

马世敏,王玉振

山东大学控制科学与工程学院, 山东济南 250061

收稿日期:2010-11-05 出版日期:2011-04-16 发布日期:2010-11-05
作者简介:马世敏(1985- ),男,广西钦州人,硕士研究生,主要研究方向为有限时间稳定. Email:mashimin@mail.sdu.edu.cn
基金资助:
国家自然科学基金资助项目(G61074068);山东省自然科学基金资助项目(ZR2010FM013);教育部高等学校博士点专项基金资助项目(G200804220028)

Finite-time stability of a class of generalized Hamiltonian systems with
application to control design of nonlinear affine systems

MA Shi-min, WANG Yu-zhen

School of Control Science and Engineering, Shandong University, Jinan 250061, China

Received:2010-11-05 Online:2011-04-16 Published:2010-11-05

摘要/Abstract

摘要：

研究了一类广义Hamilton系统的有限时间稳定性及其在仿射非线性系统控制设计中的应用,并给出几个新结果。利用Hamilton系统的结构特性和已有的关于局部有限时间稳定的结果,给出该类Hamilton系统有限时间稳定的几个判定准则。把得到的新结果应用于仿射非线性系统的有限时间控制设计中。通过选取恰当的Hamilton函数,并利用正交分解Hamilton实现及阻尼注入技术,为一类仿射非线性系统设计了一类有限时间控制器。给出两个例子以验证本文结论的有效性。

关键词: 有限时间稳定性, Hamilton系统, 阻尼注入, Hamilton实现

Abstract:

Finite-time stability was investigated for a class of generalized Hamiltonian systems with application to control design of nonlinear affine systems, and a number of new results were presented. Based on the structural properties of Hamiltonian systems and the existing results of local finitetime stability, several criteria were obtained for the finitetime stability of the class of generalized Hamiltonian systems. The obtained results were used to study the finitetime control design for a class of nonlinear affine systems. Via choosing a suitable Hamiltonian function, and utilizing the orthogonal decomposition Hamiltonian realization and the damping injection technique, a new control design procedure was established. Two illustrative examples were given to support the new results obtained in this paper.

Key words: finite-time stability, Hamiltonian systems, damping injection, Hamiltonian realization

马世敏,王玉振. 一类广义Hamilton系统的有限时间稳定性及其在仿射非线性系统控制设计中的应用[J]. 山东大学学报(工学版), 2011, 41(2): 119-125.

MA Shi-min, WANG Yu-zhen. Finite-time stability of a class of generalized Hamiltonian systems with
application to control design of nonlinear affine systems[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2011, 41(2): 119-125.

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