I know that for an LTI system having complex exponential input,
i.e, $x(t)=\exp(j w_o t)$ & $h(t) \to $ LTI System ;
then, its output { $y(t) \} =M \exp(j w_o t + \phi)$ , where $M= |H(j w)|_{|w= w_o}$ & $\phi = \angle \{ H(j w)\} _{|w= w_o}$
But for a causal LTI system having exponential input,
i.e, $x(t)=\exp(a t)$ & $h(t) \to $ Causal LTI System ;
Is it true to say its output $\{ y(t)\}$ is given by:
$y(t) =K \exp(a t )$ , where $K= H(s)_{|s=a} \quad$ ?