---
title: Control Theory
description: Control theory deals with influencing the behavior of dynamical systems using feedback loops. Learners will understand how to design controllers, analyze system stability, and optimize performance in engineering, robotics, and automated processes.
category: mathematics
subcategory: dynamical-systems
difficulty: beginner, intermediate, advanced
url: /subject/control-theory
---

# Control Theory

Control theory deals with influencing the behavior of dynamical systems using feedback loops. Learners will understand how to design controllers, analyze system stability, and optimize performance in engineering, robotics, and automated processes.

## Available Resources

2 Books • 2 Courses • 2 Websites

## Websites

### 1. MathWorks Control Tutorials

University of Michigan and Carnegie Mellon tutorials that work classic control problems, cruise control, inverted pendulum, ball and beam, through modelling, PID, root locus, frequency response and state space, with runnable MATLAB and Simulink code for each step.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ctms.engin.umich.edu/CTMS/index.php

**Tags:** control-systems, matlab, simulink, pid-control, root-locus, state-space

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Dynamic Systems and Control (MIT 6.241J)

**Author:** Emilio Frazzoli, Munther Dahleh

Analysis and control of linear time-invariant systems modeled by ordinary differential equations: state-space models, input-output response, feedback interconnections, stability and performance. Provides lecture notes, the full open textbook, and problem sets with solutions for designing controllers with guaranteed properties.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://ocw.mit.edu/courses/6-241j-dynamic-systems-and-control-spring-2011/

**Tags:** linear-systems, state-space, stability, feedback-control, robust-control

### 2. Principles of Optimal Control (MIT 16.323)

**Author:** Jonathan P. How

Deterministic and stochastic optimal control for discrete and continuous systems, covering numerical search, dynamic programming, calculus of variations, Pontryagin's maximum principle and model predictive control. Provides detailed lecture notes, problem sets, exams and programming assignments for designing optimal controllers.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://ocw.mit.edu/courses/16-323-principles-of-optimal-control-spring-2008/

**Tags:** optimal-control, dynamic-programming, model-predictive-control, calculus-of-variations, pontryagin-maximum-principle

## Books

### 1. Mathematical Control Theory

**Author:** Jerzy Zabczyk

A graduate introduction to control from a mathematician's standpoint: linear systems, controllability, stabilizability, realization theory, optimal control and dynamic programming, with rigorous proofs. Prepares readers to follow research papers in control and infinite-dimensional systems.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/9812563717?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, dynamical-systems

### 2. Control Theory for Linear Systems

**Author:** Harry L. Trentelman, Anton A. Stoorvogel, Malo Hautus

A geometric, state-space treatment of linear control synthesis: controllability and observability, stabilization, disturbance decoupling, tracking and regulation, linear quadratic regulation, and H2 and H-infinity control. Exercises extend each chapter. Assumes solid linear algebra and prior control coursework.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/1447110730?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, dynamical-systems

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