Automatica (IFAC), Accepted for Publication, Aug. 2008. Computing the L2 gain for linear periodic continuous-time systems M. Cantoni and H. Sandberg Abstract A method to compute the L2 gain is developed for the class of linear periodic continuous-time systems that admit a finite-dimensional state-space realisation. A bisection search for the smallest upper bound on the gain is employed, where at each step an equivalent discrete-time problem is considered via the well-known technique of time-domain lifting. The equivalent problem involves testing a bound on the gain of a linear shift-invariant discrete-time system, with the same state dimension as the periodic continuous-time system. It is shown that a state-space realisation of the discrete-time system can be constructed from point solutions to a linear differential equation and two differential Riccati equations, all subject to only single-point boundary conditions. These are well-behaved over the corresponding one period intervals of integration, and as such, the required point solutions can be computed via standard methods for ordinary differential equations. A numerical example is presented and comparisons made with alternative techniques. Key words: Norms, linear systems, time-varying systems, computational methods