Add to ORKGThis paper is concerned with the finite-horizon version of the H∞ problem with measurement feedback. Given a finite-dimensional linear, time-varying system, together with a positive real number γ, we obtain necessary and sufficient conditions for the existence of a possibly time-varying dynamic compensator such that the L2([0, t1])-induced norm of the closed-loop operator is smaller than γ. These conditions are expressed in terms of a pair of quadratic differential inequalities, generalizing the well-known Riccati differential equations introduced recently in the context of finite-horizon H∞ control.