ECE Course Outline

ECE4570

System Theory for Communication and Control (3-3-4)

Prerequisites
ECE 3085/3550
Corequisites
None
Catalog Description
Study of the basic concepts in linear system theory and numerical linear algebra with applications to communication, compution, control and signal processing. A unified treatment.
Textbook(s)
Brian Hall, Lie Groups, Lie Algebras, and Representations-An Elementary Introduction (1st edition), Springer-Verlag, 2003. ISBN 0387401229, ISBN 9780387401225(optional)

Topical Outline
Introduction
     Matrix algebra and algebraic structures
     State equations for linear systems

Reachability and Observability Properties
     Range space, reachability and minimum norm solution
     Null space, observability and last squared error solution
     Finite state systems and linear modular systems: cyclic codes

Solutions of State Equations
     Eigen problem
     Stability
     Quadratic forms
     Visualization

Design - Ubiquitous Feedback Principle
     Stabilization and control
     Observer design
     Stabilization and convergence of numerical algorithms
     Motion planning and steering
     Synchronization in communication systems
     Linear automata: applications in computer control, error-correcting
        codes, random number generation

Markov Chains
     Models for information sources
     Theory of finite Markov chains
     Nonnegative matrices and applications

Simulation and Modelling 
     Shift-register synthesis, BCH decoding and Berlekamp-Massey algorithm
     Subspace identification algorithm
     Parametrization and sensistivity
     Elementary notions of optimization