Nonhomogeneous GSEs

This chapter considers parametric solution to the following higher-order nonhomogeneous GSE:

i=0 BiWFi + R, (5.1)

where

■ Ai ∈ Rn×q, Bi ∈ Rn×r , i = 0, 1, . . . ,m, F ∈ Cp×p, and R ∈ Cn×p are the parameter matrices

■ V ∈ Cq×p and W ∈ Cr×p are the matrices to be determined Again, the two polynomial matrices associated with this equation are

⎧ ⎪⎪⎨

⎪⎪⎩

A(s) = m∑

i=0 Aisi, Ai ∈ Rn×q

B(s) = m∑

i=0 Bisi, Bi ∈ Rn×r .