In system theory and control, the stability of a given system is an important specification; often we design controllers with stability as the highest priority. A computationally faster algorithm for the Routh–Hurwitz criterion has been discussed in our previous work. This article focuses on computationally fast algorithms and simpler proofs of stability criteria for finite-dimensional linear time invariant (FDLTI) systems. Lyapunov introduced his famous stability theory for both linear and nonlinear systems. In this article, instead of solving the Lyapunov equation and checking its solution for sign-definiteness, we present a new way of testing stability. We rewrite the characteristic polynomial in state-space form, controller canonical form in particular, and check the negative-definiteness of the resulting non-symmetric system matrix A. We demonstrate that this approach provides a bridge between the classical approaches and more modern Lyapunov theory as far as FDLTI systems are concerned.