Solution of the state feedback singular H-infinity control problem for linear time-varying systems

In this paper we consider the singular, finite horizon, state feedback H-in finity control problem for linear time-varying systems. Singular problem me ans that the feedthrough matrix between the control input and the controlle d output is not full column rank; in this case we prove that the original H -infinity problem is equivalent to another H-infinity problem related to a reduced order system. If this problem is regular it can be solved via stand ard techniques, conversely we can iterate the reduction procedure. We show that this iterative procedure terminates when either a trivial problem is e ncountered or the last reduced order problem is nonsingular. (C) 2000 Elsev ier Science Ltd. All rights reserved.