分数阶时变广义系统稳定性分析  

Stability Analysis for Fractional Order Singular Systems with Time-varying

作　　者：杨军[1] 张倩[1] 华长春[2] 彭丹[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]燕山大学电气工程学院,河北秦皇岛066004

出　　处：《数学的实践与认识》2017年第7期254-260,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61403335);河北省应用基础研究计划重点基础研究项目(13961806D)

摘　　要：基于Caputo分数阶导数,研究了分数阶时变广义线性系统和分数阶时变广义非线性系统的稳定性问题.首先利用相关不等式,给出了一个时变广义线性系统无脉冲且稳定的充分条件.然后,通过慢子系统来判断快子系统的变化,并利用Riccati方程,建立了分数阶时变广义非线性系统是渐近稳定的判定准则.最后,给出了算例和Simulink仿真结果,以说明结论的正确性.In this paper,the problems of stability for fractional order linear singular systems and nonlinear singular systems with time-varying are studied.First of all,a sufficient condition is derived based on matrix inequality,in which linear singular system is found to be impulse-free and stable.Due to fact that the slow sub-systems can be determined by the fast sub-systems with appropriate conditions,some concise criteria of stability for nonlinear singular systems with time-varying are obtained by using Riccati equation.Finally two examples and Simulink simulations are given to illustrate the proposed results.

关 键 词：稳定性 分数阶广义系统 时变 RICCATI方程 SIMULINK 

分 类 号：O175[理学—数学]