Linear control theory and quasi-differential equations

Summary LetI be an interval of the real line, and letA andB ben×n complex-valued, Lebesgue measurable, matrix functions defined onI such thatAL _loc ¹(I) andBL _loc (I). Ifx=x₁x₂x _n ] ^t andu=u ₁ u ₂u _n ] ^t are column vectors defined onI such thatxAC _loc ¹anduL _loc ¹(I) then the linear control problem considered isx(t)=A(t) x(t)+B(t)u(t) (tI) wherex is the response, andu is the control. This paper is concerned with the problem of determining necessary and sufficient conditions onA andB to make (^*) fully controllable onI, without departing from the basic requirementsAL _loc ¹ (I) andBL _loc (I)Dedicated to Professor H.-W. Knobloch on the occasion of his sixtieth birthday