On the distributed stable full information H∞ minimax problem

We study the distributed parameter suboptimal full information Hm problem for a stable well-posed linear system with control u, disturbance w, state x, and output y. Here u, w, and y are L-2-signals on (O, infinity) with values in the Hilbert spaces U, W, and Y, and the state x is a continuous function of time with values in the Hilbert space H. The problem is to determine if there exists a (dynamic) gamma-suboptimal feedforward compensator, i.e., a compensator U such that the choice u = Uw, makes the norm of the input/output map from w to y less than a given constant y. A sufficient condition for the existence of a gamma-suboptimal compensator is that an appropriately extended input/output map of the system has a (J, S)-inner-outer factorization of a special type, and if the control and disturbance spaces are finite-dimensional and the system has an L-1 impulse response, then this condition is also necessary. Moreover, in this case there exists a central state feedback/feedforward controller, which can be used to give a simple parameterization of the set of all gamma-suboptimal compensators. Our proof use a game theory approach. (C) 1998 John Wiley & Sons, Ltd.