不确定分数阶时滞系统的鲁棒稳定性判定准则

基于退化分析方法提出一种判定准则, 用于分析不确定分数阶时滞系统的稳定性. 介绍一种分数阶积分算子的有理逼近方法, 在此基础上采用整数阶系统逼近分数阶系统, 从而将难以判定的分数阶系统稳定性问题转化为由逼近偏差作为不确定项的整数阶系统稳定性问题进行处理. 利用积分不等式法研究逼近系统稳定性, 得到LMI 形式的稳定性判据. 仿真结果表明, 所提出方法能够有效分析这类系统的稳定性.

Robust stability criteria for uncertain fractional order systems with time delay

Based on model approximation, the problem of stability analysis for uncertain fractional order systems with time-varying delay is proposed. Firstly, a rational approximation method is introduced for fractional order systems. Based on the above method, the fractional order systems are transformed into the integer order systems whose uncertainties are approximation error. Afterwards, integral inequality approach is used to analyze the stability of the approximation system, obtaining a robust stability criteria denoted by LMI. Theoretic proof and numerical examples are provided to illustrate the effectiveness and the availability of the proposed method.