Advanced Linear Systems


CMPE Degree: This course is Not Applicable for the CMPE degree.

EE Degree: This course is Not Applicable for the EE degree.

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

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

Course Coordinator:

Prerequisites: ECE 6550

Corequisites: None.

Catalog Description

Study of multivariable linear system theory and robust control design

Course Outcomes

Not Applicable

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. ( Not Applicable ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( Not Applicable ) 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. ( Not Applicable ) An ability to communicate effectively with a range of audiences

4. ( Not Applicable ) 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. ( Not Applicable ) 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. ( Not Applicable ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( Not Applicable ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

Strategic Performance Indicators (SPIs)

Not Applicable

Course Objectives

Topical Outline

1. Algebraic Preliminaries
a. Vector Spaces
b. Modules
c. Linear Transformations
2. State Space and Matrix Fraction Description of MIMO Systems
a. Polynomial Matrices and Matrix Fraction Descriptions
b. Unimodular Transformations, Hermite Form
c. Coprimeness, Smith Form
d. Rational Matrices and Smith-McMillan Form
3. MIMO State Space Realization Theory
a. Shift Operator
b. MIMO Observability and Reachability
c. Realization and Invariants
d. Toeplitz Hankel and Bezout Matrices
4. State Feedback and Compensator Design for MIMO Systems
a. Parametrization of all stabilizing controllers (Youla-Kucera)
b. State Space Analysis
c. Transfer Function Analysis
5. General Differential Systems and Polynomial Matrix Descriptions
a. System Matrices
b. System Equivalence
c. Poles and Zeros of MIMO Systems
6. Model Order Reduction for MIMO Systems
a. Singular value decomposition
b. Balanced realizations
c. Reduction by model truncation
7. Supplements, selected from
a. MIMO Linear Time-variant Systems
b. MIMO Discrete Time Periodic Systems
c. Functional Differential Equations and Differential Delay Systems
d. Graphical Frequency Response Techniques for MIMO
e. Robust Analysis and Synthesis