| Abstract: | This paper discusses the 4‐block H∞ control problem with infinite and finite jω‐axis invariant zeros in the state‐space realizations of the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output, where these realizations are induced from a stabilizable and detectable realization of the generalized plant. This paper extends the DGKF approach to the H∞ control problem but permitting infinite and finite jω‐axis invariant zeros by using the eigenstructures related to these zeros. Necessary and sufficient conditions are presented for checking solvability through checking the stabilizing solutions of two reduced‐order Riccati equations and examining matrix norm conditions related to the jω‐axis zeros. The parameterization of all suitable controllers is given in terms of a linear fractional transformation involving a certain fixed transfer function matrix and together with a stable transfer function matrix with gain less than 1 which is free apart from satisfying certain interpolation conditions. Copyright © 2000 John Wiley & Sons, Ltd. |
