A non-iterative method for computing the infimum in H∞ -optimization

Abstract

This paper presents a simple and non-iterative procedure for the computation of the exact value of the infimum in the singular H∞-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H∞-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jω axis and also satisfy certain geometric conditions. The computation of the infimum in our method involves solving two well-defined Riccati and two Lyapunov equations.