A Variational Approach to H∞ Control with Transients

©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.This paper presents a variational approach to H∞ control with transients in the state feedback case. 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 proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant (LTV) plant 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 suboptimal H∞ state feedback control can be achieved in an input–output point of view and that the performance measure γ(μ1/2 used in this paper) is a strict upper bound