Overview

Given a system of the form

(3.1)

(3.2)

the H _? optimization problem minimizes the performance index6 ^, 49:

(3.3)

where T _zv( s) is the closed-loop transfer function from the selected exogenous disturbance inputs v to selected error responses z. These inputs form a subset of the system's total input vector [v u] ^T. The errors are a subset of the total output vector [z y] ^T. The control variables used for feedback are also a subset of the input vector u, and the measurements available for feedback form another subset of the output vector y.

Additional implicit exogenous inputs can be specified using the sensor noise parameter W _2, which corresponds to disturbances (scaled by W ₂) added to selected feedback measurements.4 ^, 50 Similar error outputs can be specified by using the control weighting parameter W ₁, 51 which corresponds to selected feedback control signals (scaled by W ₁) augmented directly to the error vector. These terms are not present whenever their respective parameter, W ₁ or W ₂, is zero. They are used to generate the H _? control and filter gains, and the H _? compensator.

In general, H _? problems cannot be solved in closed form.52 Instead, a repetitive process is required using the H _? performance level ? as the iteration parameter. The design process starts with an H _? solution using a...