State-space representation (controllable canonical, observable canonical, diagonal forms), Controllability and observability tests (Popov-Belevitch-Hautus eigenvalues), Pole placement by state feedback, Ackermann's fo...
State-space representation (controllable canonical, observable canonical, diagonal forms), Controllability and observability tests (Popov-Belevitch-Hautus eigenvalues), Pole placement by state feedback, Ackermann's formula, State observers (Luenberger full-order/reduced-order), Separation principle, Riccati equation fundamentals.
Linear Quadratic Regulator (LQR) design (finite/infinite horizon), Algebraic Riccati Equation (ARE) solution, Steady-state LQR and optimal gain computation, Linear Quadratic Gaussian (LQG) control, Kalman filtering for state estimation, Loop transfer recovery (LQR/LQG trade-offs), Disturbance decoupling and regulation.
H-infinity control fundamentals (small gain theorem, bounded real lemma), Mixed-sensitivity optimization, mu-synthesis for structured uncertainty, Loop-shaping design procedure, Robust stability/performance margins, Kharitonov theorem for interval plants, Quantitative feedback theory (QFT) basics.
Model Reference Adaptive Control (MRAC: MIT rule, Lyapunov-based), Self-tuning regulators (explicit/implicit), Parameter convergence analysis, Persistent excitation conditions, Dead-zone modification for noise robustness, Gain scheduling strategies, Switching and supervisory control, Adaptive pole placement.
Feedback linearization (input-state, input-output), Sliding mode control (reaching law, boundary layer), Backstepping design for strict-feedback systems, Lyapunov stability analysis (direct/indirect methods), Passivity-based control, Model Predictive Control (MPC) fundamentals, Constrained optimization (QP solvers).