基于分数阶微分方程描述的系统的能控性和能观性判据

The Controllability and Observability Criteria of Systems Described by Fractional Differential Equations

首先给出了由分数阶微分方程描述的系统的数学模型,根据对整数阶系统能控性和能观性的研究,给出了此类分数阶系统的能控性和能观性的定义,并利用两参数的Mittage-Leffler函数和Cayley-Hamilton定理分析此类分数阶系统的能控性和能观性,推导由分数阶微分方程描述的系统能控性和能观性判据.当其能控性判别矩阵M和能观性判别矩阵N的秩为满秩时,分数阶系统是能控和能观的.

The mathematics model of the systems described by fractional differential equations is proposed. In terms of the controllability and observability analysis on integer-order linear systems, the definitions of controllability and observability for fractional-order systems are presented. The controllability and observability are mainly analyzed by using the Mittage-Leffler function in two parameters and Cayley-Hamilton theorem. The criteria of controllability and observability for such systems are derived. If the controllability criterion matrix and observability criterion matrix have full rank, then the fractional-order systems are controllable and observable.