This paper is yet another demonstration of the fact that enlarging the design space allows simpler tools to be used for analysis. It shows that several problems in linear systems theory can be solved by combining Lyapunov stability theory with Finsler’s Lemma. Using these results, the differential or difference equations that govern the behavior of the system can be seen as constraints. These dynamic constraints, which naturally involve the state derivative, are incorporated into the stability analysis conditions through the use of scalar or matrix Lagrange multipliers. No a priori use of the system equation is required to analyze stability. One practical consequence of these results is that they do not necessarily require a state space formulation. This has value in mechanical and electrical systems, where the inversion of the mass matrix introduces complicating nonlinearities in the parameters. The introduction of multipliers also simplify the derivation of robust stability tests, based on quadratic or parameter-dependent Lyapunov functions.