A rigorous approach to H/sup /spl infin// control with transients

This paper presents a variational approach to H/sup /spl infin// control with transients in the state feedback case. The problem was formulated in Khargonekar et al. (1991). 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 a finite horizon is considered first, and then the results are extended to the linear time-invariant (LTIV) plant on an infinite horizon. By this approach, it can be directly concluded that only sub-optimal H/sup /spl infin// state feedback control can be achieved from an input/output point of view and that the performance measure /spl gamma/(/spl mu//sup 1/2/ used in this paper) is a strict upper bound.