Course - Introduction to Linear Dynamical Systems

Course Level: Senior

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 behaviour. 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. Prerequisites: Exposure to linear algebra and matrices. You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.

Prerequisites
• Lecture 1 - Overview Of Linear Dynamical Systems
• Lecture 2 - Linear Functions (Continued)
• Lecture 3 - Linearization (Continued)
• Lecture 4 - Nullspace Of A Matrix (Continued)
• Lecture 5 - Orthonormal Set Of Vectors
• Lecture 6 - Least-Squares
• Lecture 7 - Least-Squares Polynomial Fitting
• Lecture 8 - Multi-Objective Least-Squares
• Lecture 9 - Least-Norm Solution
• Lecture 10 - Examples Of Autonomous Linear Dynamical Systems
• Lecture 11 - Solution Via Laplace Transform And Matrix Exponential
• Lecture 12 - Time Transfer Property
• Lecture 13 - Markov Chain (Example)
• Lecture 14 - Jordan Canonical Form
• Lecture 15 - DC Or Static Gain Matrix
• Lecture 16 - RC Circuit (Example)
• Lecture 17 - Gain Of A Matrix In A Direction
• Lecture 18 - Sensitivity Of Linear Equations To Data Error
• Lecture 19 - Reachability
• Lecture 20 - Continuous-Time Reachability