For example, consider g=1 and

It is easy to check that *X**1**=Y**1*=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 < *X**1** *< 2, 1<*Y**1* < 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.

Example