分数阶系统线性矩阵不等式稳定判据的改进与鲁棒镇定：0＜α＜1的情况  

Improved linear matrix inequalities stability criteria for fractional order systems and robust stabilization synthesis:The 0<α<1 case

作　　者：梁舒[1] 彭程[1] 王永[1] 

机构地区：[1]中国科学技术大学自动化系,安徽合肥230027

出　　处：《控制理论与应用》2013年第4期531-535,共5页Control Theory & Applications

基　　金：国家自然科学基金资助项目(61004017,60974103)

摘　　要：针对确定的分数阶系统,通过发掘其稳定区域与线性矩阵不等式(LMI)之间的联系,提出改进的LMI稳定判据.与已有结果相比,该判据形式简洁,求解变量少,且不含复矩阵变量,能够直接应用于控制器设计而不带来任何保守性,克服了原判据存在的主要缺点.然后基于该判据,进一步研究了当分数阶系统具有多胞型不确定时的鲁棒镇定控制器的设计方法.最后,仿真结果表明该方法的有效性.For deterministic fractional order systems,an improved linear matrix inequality（LMI） stability criterion is derived by exploring the relation between the stability region and the LMI.It has more concise formulation and fewer variables than the existing results.Besides,the LMI criterion contains no complex matrix variable and is directly applicable to synthesis problems,without bringing forth any conservatism;thus this criterion overcomes the major drawback of the original criterion.Furthermore,for fractional order systems with polytopic-type uncertainties,a synthesis method is proposed to obtain the robust stabilization controller.Finally,numerical examples illustrate the validity of the approach.

关 键 词：分数阶系统 不确定系统 线性矩阵不等式 鲁棒稳定 鲁棒镇定 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]