Introduction to Linear Dynamical Systems
Course SummaryThis course is an introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. (Includes a full set of video lectures.)
Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.
Reading Material1. Textbook (MIT 18.06): Introduction to Linear Algebra. 3rd ed.
Strang, Gilbert. Introduction to Linear Algebra. 3rd ed. Wellesley, MA: Wellesley-Cambridge Press, March 2003. ISBN: 0961408898.
(Click the button below to see a preview of the book)
Course Material1. Matrix primer notes
(a) Matrix primer (lecture 1 slides)
(b) Matrix primer (lecture 2 slides)
(c) Matrix primer (lecture 3 slides)
2. Crimes against matrices
3. Basic notation
4. Least squares and least norm solutions using Matlab
5. Solving general linear equations using Matlab
6. Low rank approximation and extremal gain problems