## System Theory for Communication and Control

(3-0-3-4)

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

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

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

**Technical Interest Group(s) / Course Type(s):** Systems and Controls

**Course Coordinator:** Erik I Verriest

**Prerequisites:** ECE 3550

**Corequisites:** None.

### Catalog Description

Study of the basic concepts in linear system theory and numerical linearalgebra 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.

### Student Outcomes

In the parentheses for each Student Outcome:"P" for primary indicates the outcome is a major focus of the entire course.

“M” for moderate indicates the outcome is the focus of at least one component of the course, but not majority of course material.

“LN” for “little to none” indicates that the course does not contribute significantly to this outcome.

1. ( P ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( LN ) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. ( LN ) An ability to communicate effectively with a range of audiences

4. ( LN ) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts

5. ( M ) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives

6. ( P ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( P ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

### Strategic Performance Indicators (SPIs)

Not Applicable

### Course Objectives

### Topical Outline

Introduction

Matrix algebra and algebraic structures

State equations for multi-variable 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

Adjoints

Elements of Polynomial System Theory (Algebraic System Theory)

Rings and modules of polynomials

Functional Models and Shift Spaces

Linear Systems Analysis and Design

Systems on Lie Groups (Applications to Control and Computation)

Matrix Lie Groups

Lie algebras and exponential mapping, BCH-formula

Basic Representation Theory

Applications in attitude control, switched systems and ODE-solving

Linear Systems in Disguise

Carleman Linearization

Perspective systems (Applications in computer vision)

Quaternions (Applications in Robotics, Control and Signal Processing)

Design in Control and Communication

State feedback design

State observer design

Stabilization and convergence of numerical algorithms

Motion planning and steering

Synchronization in communication systems

Simulation and Modelling

Shift-register synthesis

Subspace identification algorithm

Parametrization and sensitivity

Elementary notions of optimization