For example, consider g=1 and
It is easy to check that X1=Y1=0.5 satisfy
(i) and (ii) but not (iii). Nevertheless, we can show that = 0.7321 and thus a suboptimal controller exists for In fact, we can check that 1 < X1 < 2, 1<Y1 < 2 also satisfy (i) , (ii) and (iii). For this reason, Riccati equation
approach is usually preferred over the Riccati inequality and LMI approaches whenever possible.