Optimal control means to design a state-space controller that stabilises a feedback loop and is the solution of an optimisation problem. The linear quadratic regulation (LQR) method is based on the minimisation of a time-domain quadratic cost functional which requires to solve an algebraic Ricatti equation (ARE). The solution of the ARE is used to compute the optimal state feedback controller. If the plant is subject to disturbances and noise, a Kalman filter can be designed, which embedded in the state feedback controller, serves as a linear quadratic state-estimator (LQE). The estimator feedback gain matrix is determined so that the quadratic mean of the estimation error becomes minimal. Similar to the LQR problem, an ARE is to be solved for the stationary value of the error covariance matrix. The result is used to compute the estimator feedback gain matrix. The objective of \(\mathrm {H}_{2}\) -optimal control as well as the one of \(\mathrm {H}_{\infty }\) -optimal control is to find an admissible controller that minimises the norm of the closed-loop transfer function matrix \(\mathbf {G}(s)\) from exogenous inputs w to the control outputs z. The \(\mathrm {H}_{2}\) -norm \(||\mathbf {G}(s)||_{2}\) is a measure of the total energy corresponding to the impulse response. In contrast, \(||\mathbf {G}(s)||_{\infty }\) indicates the maximum gain, i.e. the worst case of the unwanted transfer from w to z.