The finite horizon singular time-varying $H_\infty$ control problem with dynamic measurement feedback

This paper is concerned with the finite horizon version of the $H_\infty$ problem with measurement feedback. Given a finite-dimensional linear , time-varying system, together with a positive real number $\gamma$, 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 $\gamma$. 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 $H_\infty$ control.