EE263 - Introduction to Linear Dynamical Systems

Stanford Univ. - EE263: Introduction to Linear Dynamical Systems. Taught by Professor Stephen Boyd, this course offers an introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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. (from see.stanford.edu)

Lecture 01 - An Overview of Linear Dynamical Systems
Lecture 02 - Linear Functions, Linearization
Lecture 03 - Linearization (cont.), Linear Algebra Review
Lecture 04 - Linear Algebra Review (cont.), Orthonormal Sets of Vectors
Lecture 05 - Orthonormal Sets of Vectors (cont.), Gram-Schmidt Procedure, QR Factorization
Lecture 06 - Least-Squares, Least-Squares Via QR Factorization, Least-Squares Estimation
Lecture 07 - Least-Squares Polynomial Fitting, Least-Squares System Identification
Lecture 08 - Multi-Objective Least-Squares, Regularized Least-Squares, Nonlinear Least-Squares
Lecture 09 - Least-Norm Solution, Autonomous Linear Dynamical Systems
Lecture 10 - Examples of Autonomous Linear Dynamical Systems, High Order Linear Dynamical Systems
Lecture 11 - Solution Via Laplace Transform and Matrix Exponential
Lecture 12 - Time Transfer Property, Stability, Eigenvectors and Diagonalization
Lecture 13 - Diagonalization, Jordan Canonical Form, Generalized Eigenvectors
Lecture 14 - Jordan Canonical Form, Linear Dynamical Systems with Inputs & Outputs, Transfer Matrix
Lecture 15 - Gain Matrix, Z-Transform, Symmetric Matrices, Eigenvalues of Symmetric Matrices
Lecture 16 - RC Circuit (Example), Quadratic Forms, Gain of a Matrix in a Direction, Matrix Norm
Lecture 17 - Gain Of A Matrix in a Direction, Singular Value Decomposition
Lecture 18 - Sensitivity of Linear Equations to Data Error, Controllability, State Transfer, Reachability
Lecture 19 - Reachability, Controllable System
Lecture 20 - Continuous-Time Reachability, General State Transfer, Observability and State Estimation

References
EE263 - Introduction to Linear Dynamical Systems
Instructors: Professor Stephen Boyd. Handouts. Assignments. Exams. Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems.