Non-Iterative Computation of the Infimum in H∞-Optimization for Plants with Invariant Zeros on the jw Axis

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 a continuation of our earlier work [1]-[3]. Our problem formulation in general and we do not place any restrictions on the finite and infinite zero structures of the system, and 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 problem for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular this paper extends the result of [3] by allowing these two transfer functions to have invariant zeros on the jw axis.