分数阶广义不确定系统稳定性及可镇定性  

Stability and Stabilization Analysis of Fractional-Order Singular Systems with Uncertainty

作　　者：马瑞兰[1] 林崇[1] 杨志宏[1] 

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2017年第3期46-50,共5页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金资助项目(61673227)

摘　　要：针对分数阶广义系统在微分阶数0<α<1情况下的稳定性问题,本文利用实数域上的正常分数阶系统的稳定性新判据,进一步考虑分数阶广义系统的可容许性,将正常分数阶系统稳定性条件与分数阶广义系统的特点相结合,经过适当的矩阵变换,以线性矩阵不等式的形式给出分数阶广义自治系统可容许的充分必要条件。加强所得的可容许条件,可进一步得到分数阶广义不确定系统状态反馈鲁棒可镇定的充分条件,并求得状态反馈控制率。与之前推导出的分数阶广义系统状态反馈鲁棒可镇定条件相比较,本文所得结果变量较少且适用范围较广。数值例子说明本文主要结果较之前的结果更具有效性。该研究对提高分数阶广义不确定系统的稳定性具有重要意义。In view of the stability problems of fractional-order singular systems(0<α<1),this paper considers the admissibility of fractional-order singular systems by using the new stability criterion of normal fractional-order systems. We use the stability criteria of normal fractional-order systems and notice the characteristic of singular systems to propose a necessary and sufficient condition for the admissibility of fractional-order singular systems after appropriate matrix transformations.By adopting the admissible condition,we can obtain a sufficient condition for the robust stabilization for uncertain systems through state feedback law is obtained.The present conditions are given in terms of linear matrix inequalities.The results in this paper has less variables and wider range of applications and are illustrated to be more effective by numerical examples.

关 键 词：分数阶广义系统 可容许 状态反馈 

分 类 号：O231[理学—运筹学与控制论]