EE/AEM 5231 – Lecture notes

These notes are taken by a student enrolled in the course. 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; What is the course about?

• Lecture 2: Basic system properties

• Lecture 3: State-space models; Equilibrium points; Linearization

• Lecture 4: Solution to discrete time systems; State transition matrix

• Lecture 5: Z transform; Resolvent; Transfer function

• Lecture 6: Impulse and frequency responses of DT LTI systems; State transition matrix of CT systems; Variation of constants formula

• Lecture 7: Numerical computation of the state transition matrix; Matrix exponential

• Lecture 8: Laplace transform; Impulse response and transfer function of CT LTI systems; A double-integrator example

• Lecture 9: Eigenvalue decomposition; Diagonalization of a matrix

• Lecture 10: Modal decomposition of LTI systems; Normal vs. non-normal matrices
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• Lecture 11: Review of Lecture 10; Jordan canonical form

• Lecture 12: Modal conditions for stability of LTI systems

• Lecture 13: Stability of equilibrium points of nonlinear systems

• Lecture 14: Stability via linearization

• Lecture 15: Lyapunov functions for LTI systems

• Lecture 16: Algebraic Lyapunov Equation

• Lecture 17: Signal norms

• Lecture 18: Frequency responses of LTI systems

• Lecture 19: Singular Value Decomposition; System norms
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• 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 reachability

• Lecture 23: Controllability of continuous-time systems; Observability

• Lectures 24 and 25: Pole placement; State estimation; Observer-based controller

• Lecture 26: Linear Quadratic Regulator