The course gives an introduction to modern H2 and H∞ optimal controller design, as well as to LMI-based synthesis techniques and for multi-objective design. Language: English Learning outcomes: Ability to express design specifications in terms of the H2 norm or the H∞ norm and to use LMI techniques to design controllers that meet these specifications. Familiarity with relevant tools of the LMI control toolbox for Matlab. Present syllabus: Part 1 - Optimal regulator problem with finite time horizon, Riccati differential equation - Time-varying and steady state solutions, algebraic Riccati equation, Hamiltonian system - Kalman’s identity, phase margin of LQR controllers, spectral factorization - Optimal state estimation, Kalman filter, LQG control Part 2 - Generalized plant, review of LQG control - Signal and system norms, computing H2 and H∞ norms - Singular value plots, input and output directions - Mixed sensitivity design, H∞ loop shaping, choice of weighting filters - Case study: design example flight control - Linear matrix inequalities, design specifications as LMI constraints (H2, H∞ and pole region) - Controller synthesis by solving LMI problems, multi-objective design - Robust control of uncertain systems, small gain theorem, representation of parameter uncertainty - Balanced realization and model order reduction