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# Intro to Math for Systems & Control Theory

## ECE69500

1

January 19, 2021

### Learning Objective:

After completing this course, you will be able to:
• Analyze equations involving matrices by applying algebraic concepts such as rank, nullspace, linear independence, and eigenvalues.
• Define graph properties such as diameter, degrees, and connectivity, and apply them to analyze networked systems.
• Define properties of linear systems, including controllability, observability, and stability, and apply them to design state estimators and feedback controllers.
• Define probability distributions and moments of random variables, and characterize the long-term behavior of stochastic processes
• Specify the fundamental optimality conditions for optimization problems and implement basic algorithms to find the optimizers.

### Description:

This course serves as background for ECE602, Lumped System Theory; ECE695, Epidemic Processes over Networks; and ECE695, Structure and Dynamics of Large-Scale Networks; and other similar courses. The course will make the necessary mathematical background for these courses accessible by decomposing and illustrating difficult concepts with real-world examples and problems.

The course consists of five modules: 1) Linear Algebra, 2) Basic Graph Theory, 3) Basic Control Theory, 4) Probability, and 5) Optimization.

### Topics Covered:

Automatic Control (AC)

### Prerequisites:

Linear Algebra (MA 26500 or 26266) or equivalent
ECE 302, Probabilistic Methods in Electrical and Computer Engineering or equivalent

### Homework:

Four homework assignments. Answers should be typed in LaTeX.

One quiz.

### Exams:

One comprehensive proctored final exam.

### Textbooks:

No textbook; recommended reading will be provided.

### Computer Requirements:

A computer with a webcam and microphone (built-in or USB) will be required for quiz and exam proctoring.

### Other Requirements:

MATLAB or equivalent.

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