Complete solution of the 4-block H^∞ control problem with infinite and finite jω-axis zeros

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.