 Formal sinusoidal response of an unstable linear system

Substitution $s=i\omega$ into an algebraic transfer function can produce finite amplitude and phase even when the causal system has unstable poles. It then describes a sinusoidal particular solution whose growing homogeneous response is not generically absent. A physically settled frequency response requires transient asymptotic stability; for an unstable causal transfer function, its Laplace region of convergence need not include the imaginary axis.