H∞-control and filtering with initial uncertainty for time-varying systems

Abstract

The H∞-control problem with a non-zero initial condition is considered. The initial conditions are assumed to be in some subspace. First, the H∞-problem with full information is considered, and necessary and sufficient conditions for the norm of an input-output operator to be less than a given number are obtained. A characterization of all admissible controllers is given. This result is then used to solve the general H∞-control problem and the filtering problem with initial uncertainty. The filtering problem on a finite horizon involves an estimate of the state at the final time. The set of al1 suboptimal filters is given both on finite and infinite horizons.