C-半群和李雅普诺夫方程  

C-semigroup and Lyapunov equations

作　　者：谢灵红[1] 钟小秀 

机构地区：[1]西南交通大学应用数学系,成都610031 [2]江西省赣州高级技工学校,赣州341000

出　　处：《西南民族大学学报（自然科学版）》2004年第2期131-133,共3页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：考虑线性控制系统x’(f)=Ax(f)+Bu(t)(t>0),x(0)=x0,这里A是Hilbert空间X中指数稳定的C-半群T(t)的无穷小生成元,B是Hilbert空间Y到X的有界算子,且A的豫解集非空,R(C)在X中稠密时,获得了延拓控制映射LB是李雅普诺夫方程的唯一的自伴解.We consider the linear control systems x'(t) = Ax(t) + Bu(t) (t > 0), x(0) = x0, where A is the generator of an exponentially bounded C-semigroup T(t) in a Hilbert space, B is a bounded operator from Hilbert space 7 to X, the resolvent set of A is not empty and R(C) is dence in X, and obtain that the extended controllability map LB is the unique self-adjoint solution to the Lyapunov equation.

关 键 词：C-半群 李雅普诺夫方程 指数稳定 HILBERT空间 延拓控制映射 

分 类 号：O177.1[理学—数学]