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EE263: Introduction to Linear Dynamical Systems (Stanford Univ.). 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.
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Description
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)
Course content
- Lecture 01 – An Overview of Linear Dynamical Systems Unlimited
- Lecture 02 – Linear Functions, Linearization Unlimited
- Lecture 03 – Linearization (cont.), Linear Algebra Review Unlimited
- Lecture 04 – Linear Algebra Review (cont.), Orthonormal Sets of Vectors Unlimited
- Lecture 05 – Orthonormal Sets of Vectors, Gram-Schmidt Procedure, QR Factorization Unlimited
- Lecture 06 – Least-Squares, Least-Squares Via QR Factorization, Least-Squares Estimation Unlimited
- Lecture 07 – Least-Squares Polynomial Fitting, Least-Squares System Identification Unlimited
- Lecture 08 – Multi-Objective Least-Squares, Regularized Least-Squares Unlimited
- Lecture 09 – Least-Norm Solution, Autonomous Linear Dynamical Systems Unlimited
- Lecture 10 – Examples of Autonomous Linear Dynamical Systems Unlimited
- Lecture 11 – Solution Via Laplace Transform and Matrix Exponential Unlimited
- Lecture 12 – Time Transfer Property, Stability, Eigenvectors and Diagonalization Unlimited
- Lecture 13 – Diagonalization, Jordan Canonical Form, Generalized Eigenvectors Unlimited
- Lecture 14 – Jordan Canonical Form, Linear Dynamical Systems with Inputs & Outputs Unlimited
- Lecture 15 – Gain Matrix, z-Transform, Symmetric Matrices Unlimited
- Lecture 16 – RC Circuit (Example), Quadratic Forms, Gain of a Matrix in a Direction Unlimited
- Lecture 17 – Gain Of A Matrix in a Direction, Singular Value Decomposition Unlimited
- Lecture 18 – Sensitivity of Linear Equations to Data Error, Controllability, State Transfer Unlimited
- Lecture 19 – Reachability, Controllable System Unlimited
- Lecture 20 – Continuous-Time Reachability, General State Transfer, Observability Unlimited
Instructor
