  This paper deals with the certification problem for robust quadratic
stability, robust state convergence, and robust quadratic performance of linear
systems that exhibit bounded rates of variation in their parameters. We
consider both continuous-time (CT) and discrete-time (DT) parameter-varying
systems. In this paper, we provide a uniform method for this certification
problem in both cases and we show that, contrary to what was claimed
previously, the DT case requires a significantly different treatment compared
to the existing CT results. In the established uniform approach, quadratic
Lyapunov functions, that are affine in the parameter, are used to certify
robust stability, robust convergence rates, and robust performance in terms of
linear matrix inequality feasibility tests. To exemplify the procedure, we
solve the certification problem for $\mathscr{L}_2$-gain performance both in
the CT and the DT cases. A numerical example is given to show that the proposed
approach is less conservative than a method with slack variables.
