This paper investigates 2D mixed continuous-discrete-time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set. It is shown that a nonconservative linear matrix inequality (LMI) condition for ensuring robust stability can be obtained by introducing complex Lyapunov functions depending polynomially on the uncertain vector and a frequency. Moreover, it is shown that nonconservative LMI conditions for establishing upper bounds of the robust H-infinity and H-2 norms can be obtained by introducing analogous Lyapunov functions depending rationally on the frequency. Some numerical examples illustrate the proposed methodology. (C) 2016 Elsevier Ltd. All rights reserved.