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 forIn 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.