INC692: Optimal and Robust Control

Dr.-Ing. Sudchai Boonto, KMUTT, 2013

Matrix

• Identify I

$$(I-XY)^{-1}W = W + XY(I-XY)^{-1}W$$

• Proof

$$\begin{aligned} (I-XY)^{-1}W &= W - W + (I-XY)^{-1}W \\ &= W + ( -(I -XY) + I)(I-XY)^{-1}W \\ &= W + XY(I-XY)^{-1}W \end{aligned}$$