Noniterative computation of infimum in Hinfinity optimisation for plants with invariant zeros on the j omega -axis

A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H_infinity -optimisation problem is presented, as a continuation of earlier work (Chen. Saberi, and Ly, 1992). The authors´ problem formulation is general and they do not place any restrictions in 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. The method is applicable to a class of singular H_infinity -optimisation problems 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, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the j omega -axis.