Abstract
This 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 L 2([0, t 1])-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.
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