一类延滞方程的可控性

The controllability of a class of retard differential equation

摘要: 本文考虑如下带控制项的延滞方程ｘ（ｔ）＝ ∫ｒ０［ｄＨ（τ）ｘ（ｔ－ τ）］＋Ｂｕ（ｔ），并具有初始条件ｘ（θ）＝ φ（θ），θ∈［－ｒ，０］，利用最近非自反Ｂａｎａｃｈ空间上共轭Ｃ０半群的扰动理论，在Ｘ＝Ｃ（［－ｒ，０］；Ｒｎ）上得到了其近似可控的充分必要条件．

Abstract: In this paper,we consider the following retard differential equation with control term: (t)=∫ r 0 d H(τ)x(t-τ)+Bu(t),x(θ)=φ(θ),θ∈-r,0. By means of the perturbation theory of dual C 0-semigroup in non-reflective Banach space C(-r,0,R n),we obtain the necessary and sufficient condition of approximate controllability for above system.