摘要
双线性系统是一类特殊的非线性系统,广泛存在于现实世界中,如工程、经济、生物、生态等领域,被认为是最接近于线性系统的非线性系统.对双线性系统的研究已历经了近半个世纪.作为系统最基本的属性,双线性系统可控性的研究一直以来是热点和难点.本文分别对连续双线性系统可控性和离散双线性系统可控性进行讨论,综述了双线性系统可控性的研究.特别地,报告了近来对离散双线性系统可控性研究的新成果.最后,例举了一些可控的双线性系统例子.
Bilinear systems are a special class of nonlinear systems, which are widely existing in real world, such as engineering, economics, biology, ecology, etc. Among nonlinear systems, bilinear systems are thought to be the most close to linear systems. The study on such systems has passed through nearly half a century. For the fundamental property, the controllability of bilinear systems has received considerable attention, while the difficulties and challenges still remain. The purpose of this paper is to give a survey on the controllability of bilinear systems through the discussion on the controllability of continuous-time bilinear systems and discrete-time bilinear systems, respectively. Particularly, new results on the controllability are reported for discrete-time bilinear systems. Finally, some examples of controllable bilinear systems are provided.
出处
《自动化学报》
EI
CSCD
北大核心
2011年第9期1040-1049,共10页
Acta Automatica Sinica
基金
国家重点基础研究发展计划(973计划)(2010CB327904)
国家自然科学基金(60874044)资助~~
关键词
双线性系统
可控性
临近可控性
李群
拿代数
Bilinear systems, controllability, near-controllability, Lie groups, Lie algebras
