In the theory of optimal control, the linear quadratic (LQ) optimal problem plays an important role due to its physical meaning, and its solution is easily given by an algebraic Riccati equation. This solution turns out to be restrictive, however, because of two assumptions: the system must be free from disturbances and the entire state vector must be known. A new technique, called  output integral sliding modes, eliminates the effects of disturbances acting in the same subspace as the control. By using LQ-optimal control together with integral sliding modes, the former is made robust and based on output information only. Thus optimal control theory improves its applicability.