I read in a paper that solution of a differential equation $$\dot{x}(t) = -cx(t-h)+f(t)$$ where $x$ is a scalar with zero initial condition (for all $t\leq 0$) can be written as $$x(t) = \int_0^t f(\hat{t})\sum_r{\frac{e^{s_r(t-\hat{t})}}{1+h\,s_r}}d\hat{t}.$$ Here $\{s_r\}$ are solution of characteristic equation $s+ce^{-hs}=0$.
How can this be generalized to system of differential equations with zero initial condition? For example, $$\dot{z}(t) = A\,z(t-h)+B\,z+v\, f(t),$$ where $z$ is a vector. In other words how can we write the solution in terms of characteristic equation roots and integral involving function $f$.