•(i) Together with (ii)
guarantees that the two H2AREs have nonnegative stabilizing solutions.
•(ii) Necessary and
sufficient for G to be internally stabilizable.
penalty on z
= C1x + D12u includes a nonsingular, normalized penalty on the control u.
In the conventional H2setting this means that there is no cross
weighting between the state and control and that the control weight matrix is
includes both plant disturbance and sensor noise, these are orthogonal, and the sensor
noise weighting is normalized and nonsingular.