Riccati Differential Inequalities: Suboptimal H-infinity Controllers for Finite Horizon Time-Varying Systems

In this paper we give a direct derivation of the solution to the continuous time finite horizon H-infinity synthesis problem. An explicit separation of the time domain cost function into past and future pieces is used. Perturbations are made to these pieces which lead to Riccati differential inequalities in the form of the solution, and demonstrate the correspondence between the inequalities and the cost function halves.