These notes are taken by your TA. They are not edited and I am providing them in order to give you an idea of what is going on in the class.
Lecture 1: Course mechanics; Basic system properties
Lecture 2: State-space models
Lecture 3: Equilibrium points; Linearization
Lecture 4: Solution to discrete time systems; State transition matrix
Lecture 5: Z transform; Transfer function, impulse and frequency responses of DT LTI systems
Lecture 6: Solution to continuous time systems; State transition matrix
Lecture 7: Numerical computation of state transition matrix; Matrix exponential; Laplace transform
Lecture 8: A double-integrator example
Lecture 9: Eigenvalue decomposition; Diagonalization of a matrix
Lecture 10: Modal contribution to a response of an LTI system; Normal vs. non-normal matrices
Lecture 11: Modal conditions for stability of LTI systems
Lecture 12: Stability of equilibrium points of nonlinear systems
Lecture 13: Stability via linearization
Lecture 14: Stability via Lyapunov direct method
Lecture 15: Lyapunov direct method for LTI systems; Algebraic Lyapunov Equation
Lecture 16: Input-output norms (intro)
Lecture 17: Singular value decomposition
Lecture 18: Singular value decomposition (continued)
Lecture 19: Frequency responses of multivariable systems
Lecture 20: Reachability of discrete-time systems; Kalman rank test
Lecture 21: Reachability gramian; Minimum energy state transfer; Reachability ellipsoid
Lecture 22: Canonical form of unreachable systems; Modal tests for reachibility
Lecture 23: Controllability of continuous-time systems; Observability
Lecture 24: Pole placement; State estimation
Lecture 25: Observer-based controller
Lecture 26: Linear Quadratic Regulator