# InfoCoBuild

## EE263 - Introduction to Linear Dynamical Systems

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. 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)

 An Overview of Linear Dynamical Systems

 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.