We study the robust stability of linear systems with several uncertain (complex, real) scalar parameters. Using quadratic Lyapunov functions depending polynomially upon the parameters, one is able to exhibit a countable family of LMIs such that: 1) solvability of one of them is sufficient for robust stability; and 2) reciprocally, robust stability implies their solvability, except possibly for a finite number of them. This extends the characterization by the solvability of Lyapunov inequality of the asymptotic stability of usual systems. The related issue of delay-independent stability for linear systems with multiple delays is also treated, and it is shown how the approach used is linked to the search for quadratic Lyapunov-Krasovskii functional of a special type.