• (i)
Together with (ii) guarantees that the two H2 AREs have nonnegative
stabilizing solutions.
• (ii)
Necessary and sufficient for G to be internally stabilizable.
• (iii) The
penalty on z
= C1x + D12u includes a nonsingular, normalized penalty on the
control u. In the conventional H2 setting this means that
there is no cross weighting between the state and control and that the control
weight matrix is the identity.
• (iv) w
includes both plant disturbance and sensor noise, these are orthogonal, and
the sensor noise weighting is normalized and nonsingular.
• These
assumptions simplify the theorem statements and proofs, and can be
relaxed..