Course layout
Week 1: Introduction to Linear systems with Examples
Week 2: Math Preliminaries I - Vector Spaces, Bases, Coordinate Transformation, Invariant Subspaces, Inner product, Norms
Week 3: Math Preliminaries II - Rank, Types of Matrices, Eigen values, Eigen vectors, Diagonalization, Matrix Factorization
Week 4: State Transition Matrix, Solutions to LTI Systems, Solutions to LTV Systems
Week 5: Equilibrium points, Linearization, Types of Linearization with Examples
Week 6: Stability, Types of Stability, Lyapunov Equation
Week 7: Controllability, Reachability, Stabilizability, Tests, Controllable and Reachable Subspaces, Grammians, Controllable Decomposition
Week 8: Observability, Constructibility, Detectability, Tests, Subspaces, Grammians, State Estimation, Observable Decomposition
Week 9: Kalman Decomposition, Pole Placement, Controller Design
Week 10: Observer Design, Duality, Minimal Realization
Week 11: Basics of Optimal Control, LQR, Ricatti Equation
Week 12: LMIs in Control
Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.
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