多阶分数线性系统的分析与综合

项目名称： 多阶分数线性系统的分析与综合

项目编号： No.61463002

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 徐登国

作者单位： 楚雄师范学院

项目金额： 39万元

中文摘要： 近几十年来，分数阶微积分理论在实际科学与工程中的应用越来越多，已经成为学者们广泛关注的一个热门课题。分数阶控制系统是传统整数阶控制系统的扩展，目前已在力学、电学、医学工程等领域得到了应用。对于单阶分数线性系统，目前已经有比较丰富的研究成果，其理论已经日渐成熟，而对多阶分数线性系统的研究成果还相对较少。本项目以多阶分数线性系统为研究对象，以Laplace变换、Mittag-Leffler函数、分段正交函数和运算矩阵等为工具，探讨这类系统分析与综合的相关理论。首先，研究多阶分数线性系统能控与能观的条件，以及系统的对偶关系。其次，探讨多阶分数线性系统与其相应等价系统在性能上的关系，以及系统的结构分解问题。再次，研究多阶分数线性系统稳定性与能镇定的条件，以及多阶分数线性区间系统的鲁棒稳定性与鲁棒镇定问题。将单阶分数线性系统分析与综合的理论扩展到多阶的情形，为此类系统进一步的应用奠定理论基础。

中文关键词： 多阶分数线性系统；能控性；能观性；稳定性；鲁棒镇定

英文摘要： In recent decades，factional calculus theory is applied more and more in science and engineering, so that it has become a hot topic and attracted increasing interest. Fractional order control systems are the extension of traditional integer order control systems. Fractional order control systems have now been applied in mechanics, electrical, medical engineering, and so on. There are abundant research results in commensurate order fractional linear systems. The theory of commensurate order fractional linear systems has been gradually perfect. But the results of multi- order fractional linear systems are relatively less. The project takes multi-order fractional linear systems as the research objects. By using the Laplace transform, Mittag-Leffler function, piecewise orthogonal function and operational matrix , we investigate the related theory of analysis and synthesis in this kind of systems . Firstly, conditions of controllability and observability for multi-order fractional linear systems and the dual relationship of the systems will be studied. Secondly, we will explore the relationship between the multi-order fractional linear systems and the corresponding equivalent systems in performance. And the systems structure decomposition problem will be discussed. Thirdly, stability and stabilization conditions of multi-order fractional linear systems will be considered, as well as the robust stability and robust stabilization for multi-order fractional linear interval systems.The extension of analysis and synthesis of commensurate order fractional linear systems to multi-order case lay the theoretical foundation for the further applications of such systems.

英文关键词： multi-order fractional linear systems;controllability;observability;stability;robust stabilization