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: Leastsquares approximations of overdetermined equations and leastnorm 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. Multiinput multioutput systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability,
state transfer, and leastnorm inputs. Observability and leastsquares 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.), GramSchmidt Procedure, QR Factorization 
Lecture 06  LeastSquares, LeastSquares Via QR Factorization, LeastSquares Estimation 
Lecture 07  LeastSquares Polynomial Fitting, LeastSquares System Identification 
Lecture 08  MultiObjective LeastSquares, Regularized LeastSquares, Nonlinear LeastSquares 
Lecture 09  LeastNorm 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, ZTransform, 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  ContinuousTime 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.
