带分布型时滞的分数阶控制系统能观性的条件  

Observability of Fractional Dynamical Systems with Distributed Delays

作　　者：朱彦[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230039

出　　处：《五邑大学学报（自然科学版）》2012年第3期23-27,共5页Journal of Wuyi University(Natural Science Edition)

基　　金：教育部博士点基金资助项目(20113401110001)

摘　　要：通过Mittag-Leffler矩阵函数构造的能观性Gram矩阵和Cayley-Hamilton定理获得了一类带Caputo导数、具有分布型时滞的分数阶控制系统cDαx(t)=Ax(t)+integral from n=-h to 0(dxB(t,x)u(t+x)),t∈J:=J/{t1,t2,…tk},J:=[0,T],y(t)=Cx(t)+Du(t),x(0)=x0, 具有能观性的2个充要条件:1)系统在[0,t f]上,存在时刻tf>0,使Gram矩阵W0[0,tf]=integral from n=0 to tf(Eα(AT tα)CTCEα(A tα)dt)非奇异;2)若系统的能观性判别矩阵为Q0{C CA … CA(n-1)},则rankQ0=rank{C CA … CA(n-1)}=n时,系统是能观的.The paper studies on the observability of fractional dynamical systems with distributed delays cDαx（t）=Ax（t）＋integral from n=-h to 0（dxB（t,x）u（t＋x））,t∈J：=J/{t1,t2,…tk},J：=[0,T],y（t）=Cx（t）＋Du（t）,x（0）=x0 where cDα is the Caputo fractional derivative.By using the observability Gram matrix which is defined by Mittag Leffler matrix function and Cayley-Hamilton theorem,some sufficient conditions of observability are obtained：1） The system is observable on [0,tf]if and only if the observability Gammian matrix W0[0,tf]=integral from n=0 to tf（Eα（AT tα）CTCEα（A tα）dt） is non-singular,for some tf〉0;2） The system is observable on [0,tf] if and only if rankQ0=rank{C CA … CA（n-1）}=n.

关 键 词：分数阶控制系统 CAPUTO导数 分布型时滞 能观性 格拉姆矩阵 

分 类 号：O175.8[理学—数学]