A rigorous approach to H-infinity control with transients

This paper presents a variational approach to H-infinity control with transients in the state feedback case. The problem was formulated in [11]. The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are also proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant plant (LTV) on finite horizon is considered first, and then the results are extended to the linear time-invariant (LTIV) plant on the infinite horizon. By this approach, it can be directly concluded that only sub-optimal H-infinity state feedback control can be achieved in an input/output point of view and that the performance measure gamma (mu(1/2) used in this paper) is a strict upper bound.