Linear Systems Theory

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