EENG442/E&AS902/AMTH342 – LINEAR SYSTEMS – Fall 2006
Instructor: A. S. Morse, 212 Malone Lab., X24295, mailto:email@example.com
Teaching Assistant: Jia Fang, 5202B Malone Lab, X26555, mailto:firstname.lastname@example.org
Brief Summary: This is an introductory course about finite-dimensional, continuous and discrete-time linear dynamical systems. The course is intended for students interested in the systems, information, and computer sciences including robotics, control theory, signal and image processing, computer vision. The course is open to all students. Undergraduates interested in taking the course should first contact the course instructor.
Organization: The course meets on Mondays and Wednesdays from 1:00pm to 2:30pm in Malone 217. There are approximately eleven weekly homework assignments. There is a mid-term and a final exam. Review sessions will be scheduled from time to time.
Course Text: Linear System Theory, W. J. Rugh, Prentice Hall, 1996
Class Notes: Lecture Notes on Linear Algebra, Linear Differential Equations, and Linear Systems; A. S. Morse.
Week 1: Matrix algebra: fields and polynomial rings, Gauss elimination.
Week 2: Linear algebra: subspaces and linear transformations .
Week 3: Basic concepts from analysis - normed spaces, continuity, convergence
Week 6: Inner product spaces, orthogonal projections, normal matrices, symmetric and orthogonal matrices.
Week 7: Continuous and discrete-time linear systems; sampled systems; the concept of a realization.
Week 8: Controllability: reachable states, control reduction, controllable decompositions.
Week 9: Observability: unobservable states, observability reduction; minimal systems.
Week 10: Transfer matrix realizations; via partial fractions; via control canonical form; minimal realizations; isomorphic systems.
Week 11: Uniform and exponential stability; stability of continuous and discrete time-invariant systems,
Week 12: Feedback control: state-feedback, spectrum assignment, observers, observer-based control systems