SYLLABUS

EENG442/E&AS902/AMTH342 – LINEAR SYSTEMS – Fall 2006

Instructor: A. S. Morse,  212 Malone Lab.,   X24295,     mailto:morse@sysc.eng.yale.edu

Teaching Assistant:  Jia Fang,  5202B Malone Lab, X26555,   mailto:jia.fang@yale.edu

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.

Contents:

  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 4:  Linear differential equations: linearization, state-transition matrix, variation of constants formula, periodic systems.

  Week 5:  Matrix similarity, matrix exponentials, characteristic polynomial, Cayley Hamilton Theorem, Jordan normal form.

  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,

Routh-Hurwitz test , Lyapunov stability ,  perturbed systems.

Week 12:  Feedback control:  state-feedback, spectrum assignment, observers, observer-based control systems