A variational approach to H-infinity control with transients

This paper presents a variational approach to H-infinity control with trans ients in the state feedback case, The approach here provides a precise desc ription with equality, instead of inequality, in the necessary and sufficie nt conditions for the existence of a linear controller, Furthermore, the so lution existence and uniqueness are proved in terms of certain properties o f the indefinite Riccati equations derived in this paper. The linear time-v ariant (LTV) plant on finite horizon is considered first, and then the resu lts are extended to the linear time-invariant (LTIV) plant on the infinite horizon. By this approach, it can be directly concluded that only suboptima l H-infinity state feedback control can be achieved in an input-output poin t of view and that the performance measure gamma (mu(1/2) used in this pape r) is a strict upper bound.