On normal control processes

Abstract

Control processes of the form$\dot x - A(t) x = B(t) u(t)$, which are normal with respect to the unit ballB _{p′, r′} of the control spaceL ^p′([τ, T]),l ^r_m ′ are characterized in terms ofH(t)=X(T)X ⁻¹(t),B(t),X(t) any fundamental matrix solution of$\dot x - A(t)x = 0$, and directly in terms ofA, B, when bothA andB are independent oft.