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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.
Based on the degenerate analysis method, a criterion is proposed to analyze the stability of uncertain fractional-order delay systems. A rational approximation method for fractional integral operators is introduced. Based on this, an integer order system is used to approximate fractional order systems, The stability problem of fractional order system which is difficult to be determined is transformed into the problem of stability of integer order system which is approximated by the uncertainty as an indefinite item.Applying the integral inequality method to study the stability of approximation system, the stability criterion of LMI form is obtained. The results show that the proposed method can effectively analyze the stability of such systems.