Linear Multivariable Control

These are (work-in-progress) course notes for University of Washington AA/EE/ME 548 and AE 513.

Overview

This course provides a bridge between fundamental theory and practical tools in multivariable control, with a focus on both continuous and discrete-time systems. Alongside foundational topics, we will explore connections to modern learning-based control methods, complementing classical optimization-based approaches. The goal is to equip you with the essential skills needed to model complex dynamical systems and design robust controllers—preparing you for further work in control theory, robotics, and optimization.

Success in this class requires a solid background in linear algebra, multivariable calculus, and graduate-level systems theory (such as AA/EE/ME 547 or equivalent), as well as familiarity with ordinary differential equations, feedback control, and scientific computing.

Throughout the course, we will emphasize the use of modern computational tools—enabling you to implement and analyze control strategies by integrating theory with hands-on experience.

By the end of this course, you will be able to:

• Analyze the stability and performance of control systems using mathematical tools.

• Apply state-space methods to model and control multivariable systems.

• Utilize computational software to simulate and validate control designs.

• Understand and evaluate trade-offs in control system design.

• Formulate control synthesis problems and mathematically articulate control objectives and requirements.

• Become proficient with modern software tools that make real-time control possible.

Acknowledgement

This jupyter book template is based on the deep learning for molecules & materials notes by Andrew D. White.