CLOSED-FORM SOLUTIONS TO A CLASS OF H-INFINITY-OPTIMIZATION PROBLEMS

A closed-form solution is presented to the H(infinity) sub-optimal con trol problem via state or output feedback. The problem formulation is general and does not impose any restrictions on feedthrough terms betw een the control input and the controlled output or between the disturb ance input and the measurement output variables. It is, however, requi red that both the transfer function from the disturbance input to the measurement output and the transfer function from the control input to the controlled output have no invariant zeros on the jomega axis and that they satisfy certain geometric conditions. For the same class of systems, the conditions under which H(infinity) optimal control proble m, via state feedback, has a solution are given. Moreover, explicit ex pressions for the optimal solutions are provided. Finally, the pole/ze ro cancellations in the closed-loop system resulting from the H(infini ty) optimal or sub-optimal state or output feedback are examined.