System Theory for Communication and Control

(3-0-3-4)

CMPE Degree: This course is Selected Elective for the CMPE degree.

EE Degree: This course is Selected Elective for the EE degree.

Lab Hours: 0 supervised lab hours and 3 unsupervised lab hours.

Technical Interest Groups / Course Categories: Threads / ECE Electives

Course Coordinator: Erik I Verriest

Prerequisites: ECE 3085 [min D] or ECE 3084 [min D] or ECE 3550 [min D]

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)

Lie Groups, Lie Algebras, and Representations-An Elementary Introduction, A Polynomial Approach to Linear Algebra

Course Outcomes

Detect and exploit mathematical structure to solve complex problems (exact and approximation) in systems theory.

Apply common proof techniques to verify the validity of (simple) conjectures .

Apply basic principles (such as feedback) in a broad context of engineering.

Exploit geometric structure and symmetries in system and signal models to reduce hard problems to simpler ones. 

Synthesize complex processes with elementary building blocks.

Solve engineering problems through teamwork.

Strategic Performance Indicators (SPIs)

N/A

Topic List

  1. Introduction
    1. Matrix algebra and algebraic structures
    2. State equations for multi-variable linear systems
  2. Reachability and Observability Properties
    1. Range space, reachability, and minimum norm solution
    2. Null space, observability, and last squared error solution
    3. Finite state systems and linear modular systems: cyclic codes
  3. Solutions of State Equations
    1. Eigen problem
    2. Stability
    3. Quadratic forms
    4. Adjoints
  4. Elements of Polynomial System Theory (Algebraic System Theory)
    1. Rings and modules of polynomials
    2. Functional Models and Shift Spaces
    3. Linear Systems Analysis and Design
  5. Systems on Lie Groups (Applications to Control and Computation)
    1. Matrix Lie Groups
    2. Lie algebras and exponential mapping, BCH-formula
    3. Basic Representation Theory
    4. Applications in attitude control, switched systems and ODE-solving
  6. Linear Systems in Disguise
    1. Carleman Linearization
    2. Perspective systems (Applications in computer vision)
    3. Quaternions (Applications in Robotics, Control and Signal Processing)
  7. Design in Control and Communication
    1. State feedback design
    2. State observer design
    3. Stabilization and convergence of numerical algorithms
    4. Motion planning and steering
    5. Synchronization in communication systems
  8. Simulation and Modelling
    1. Shift-register synthesis
    2. Subspace identification algorithm
    3. Parametrization and sensitivity
    4. Elementary notions of optimization