Complete solution of the 4-block H-infinity control problem with infinite and finite j omega-axis zeros

This paper discusses the 4-block H-infinity control problem with infinite a nd finite j omega-axis invariant zeros in the state-space realizations of t he transfer functions from the control input to the controlled output and f rom the disturbance input to the measurement output, where these realizatio ns are induced from a stabilizable and detectable realization of the genera lized plant. This paper extends the DGKF approach to the Hm control problem but permitting infinite and finite j omega-axis invariant zeros by using t he eigenstructures related to these zeros. Necessary and sufficient conditi ons are presented for checking solvability through checking the stabilizing solutions of two reduced-order Riccati equations and examining matrix norm conditions related to the j omega-axis zeros. The parameterization of all suitable controllers is given in terms of a linear fractional transformatio n involving a certain fixed transfer function matrix and together with a st able transfer function matrix with gain less than 1 which is free apart fro m satisfying certain interpolation conditions. Copyright (C) 2000 John Wile y & Sons, Ltd.